## VERTEX FORM OF A QUADRATIC FUNCTION WORKSHEET

1. Write the quadratic function in vertex form whose graph is shown below.

Questions 2-4 : Write the quadratic function in vertex form and write its vertex.

2. f(x) = x 2 + 6x + 9

3. f(x) = -x 2 - 2x - 2

4. f(x) = 4x 2 + 16x + 5

5. Write the following quadratic function in vertex form and sketch its graph :

f(x) = -x 2 + 2 x + 3

1. Answer :

The parabola above opens up with vertex (2, 1).

Vertex form of a quadratic function :

f(x) = a(x - h) 2 + k

Substitute vertex (h, k) = (2, 1).

f(x) = a(x - 2) 2 + 1 ----(1)

The y-intercept of the parabola is (0, 5). That is, the parabola is passing through (0, 5).

Substitute x = 0 and y = 5.

5 = a(0 - 2) 2 + 1

5 = a(- 2) 2 + 1

5 = 4a + 1

Subtract 1 from both sides.

Divide both sides by 4.

Substitute a = 1 in (1).

f(x) = 1(x - 2) 2 + 1

2. Answer :

Vertex form of the quadratic function :

f(x) = x 2 + 6x + 9

f(x) = x 2 + 2(x)(3) + 3 2

f(x) = (x + 3) 2

Comparing y = a(x - h) 2 + k and f(x) = (x + 3) 2 ,

h = -3 and k = 0

So, the vertex is (h, k) = (-3, 0).

3. Answer :

f(x) = -x 2 - 2 x - 2

f(x) = -(x 2 + 2x) - 2

f(x) = -[x 2 + 2(x)(1) + 1 2 - 1 2 ] - 2

f(x) = -[(x + 1) 2 - 1 2 ] - 2

f(x) = -[(x + 1) 2 - 1] - 2

f(x) = -(x + 1) 2 + 1 - 2

f(x) = -(x + 1) 2 - 1

Comparing f(x) = a(x - h) 2 + k and f(x) = -(x + 1) 2 - 1,

h = -1 and k = -1

So, the vertex is (h, k) = (-1, -1).

4. Answer :

f(x) = 4x 2 + 16x + 5

f(x) = 4(x 2 + 4x) + 5

f(x) = 4[x 2 + 2(x)(2) + 2 2 - 2 2 ] + 5

f(x) = 4[(x + 2) 2 - 2 2 ] + 5

f(x) = 4[(x + 2) 2 - 4] + 5

f(x) = 4(x + 2) 2 - 16 + 5

f(x) = 4(x + 2) 2 - 11

Comparing f(x) = a(x - h) 2 + k and f(x) = 4(x + 2) 2 - 11,

h = -2 and k = -11

So, the vertex is (h, k) = (-2, -11).

5. Answer :

Vertex form of the quadratic equation :

f(x) = -(x 2 - 2x) + 3

f(x) = -[x 2 - 2(x)(1) + 1 2 - 1 2 ] + 3

f(x) = -[(x - 1) 2 - 1 2 ] + 3

f(x) = -[(x - 1) 2 - 1] + 3

f(x) = -(x - 1) 2 + 1 + 3

f(x) = -(x - 1) 2 + 4

Comparing f(x) = a(x - h) 2 + k and f(x) = -(x - 1) 2 + 4,

h = 1 and k = 4

So, the vertex is (h, k) = (1, 4).

To graph the above quadratic equation, we need to find x-intercept and y-intercept, if any.

x-intercept :

To find the x-intercept, substitute f(x) = 0.

0 = -(x - 1) 2 + 4

(x - 1) 2 = 4

Take square root on both sides.

x - 1 = ±√4

x - 1 = ±2

x - 1 = -2 or x - 1 = 2

x = -1 or x = 3

So, the x-intercepts are (-1, 0) and (3, 0) .

y-intercept :

To find the y-intercept, substitute x = 0.

f(0) = -(0 - 1) 2 + 4

= -(-1) 2 + 4

= -1 + 4

So, the y-intercept is (0, 3).

Comparing f(x) = a(x - h) 2 + k and f(x) = -(x - 1) 2 + 4,

So, the parabola opens down with vertex (1, 4), x-intercepts (-1, 0) and (3, 0) and y-intercept (0, 3).

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## Practice Worksheet Graphing Quadratics In Vertex Form

Practice Worksheet Graphing Quadratics In Vertex Form – This Quadratic Worksheet will help you with quadratic equations. It will help you learn how to solve quadratic equations by using the quadratic formula. This formula is the most efficient way to solve quadratic equations. There are however other methods to solve quadratic problems, such as graphing, factoring or completing the square. To make solving quadratic equations more efficient, algorithms were developed.

A quadratic worksheet will also help you learn how to find the sum, product, and discriminant of quadratic equations. Students will use the free printable worksheets to solve quadratic equations and practice identifying the nature and number of roots. The worksheets also teach students how to solve MCQs.

Quadratic worksheets will aid students in developing a solid understanding and confidence in solving quadratic equations. This worksheet is great for reviewing what students have learned and to evaluate their progress. In addition, the worksheet will help students become more independent as they get more practice solving quadratic equations.

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Algebra 1 Course: Algebra 1 > Unit 14 Vertex form introduction Math > Algebra 1 > Quadratic functions & equations Graph quadratics in vertex form Google Classroom You might need: Calculator Graph the function. g ( x) = 1 3 ( x − 6) 2 + 1 1 2 3 4 5 6 7 8 9 − 2 − 3 − 4 − 5 − 6 − 7 − 8 − 9 1 2 3 4 5 6 7 8 9 − 2 − 3 − 4 − 5 − 6 − 7 − 8 − 9 y x

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Exercise 3.1e. J. ★ Use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. ★ Write the equation of the quadratic function that contains the given point and has the same shape as the given function. 231) Contains (1, 1) and has shape of f(x) = 2x2.

Worksheet by Kuta Software LLC Algebra 2 Honors - Mr. Allen-Black Quadratics in Vertex Form - Practice Name_____ ID: 1 Date_____ Period____ ©x Z2e0h1x8t MKtugtlaD LSRoWfItjwQa`rMeF ELLLwCh.H n FAAlQlH jryijgkhttBsx brlezsNewrCvceDdo.-1-Sketch the graph of each function. USE PENCIL ONLY!! If you need help, use a graphing calculator, or go to ...

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Quadratic word problems (vertex form) Google Classroom. You might need: Calculator. Shenelle has 100 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width x (in meters) is modeled by: A ( x) = − ( x − 25) 2 + 625.

parabola is, we are comparing the parabola to the parent quadratic function of . y = x², which has a standard width of a=1. The smaller the absolute value of a, the . wider the parabola will be. Use your calculator to graph the parent function, y = x². Then, graph the following four quadratic equations on your calculator and compare their ...

Practice Worksheet: Graphing Quadratic Functions in Vertex Form For #1-6, label the axis of symmetry, vertex, y-intercept, and at least three more points on the graph. Write the equation of the parabola in vertex form.

Graphing quadratics: vertex form Google Classroom About Transcript Learn how to graph any quadratic function that is given in vertex form. Here, Sal graphs y=-2 (x-2)²+5. Created by Sal Khan. Questions Tips & Thanks Want to join the conversation? Sort by: Top Voted ☭СССР☭ 9 years ago

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This 8-question algebra 1 worksheet provides students with organized practice graphing quadratics in Vertex Form. Students will first identify the vertex and then complete a table of values in order to graph the parabola. I have also provided an option that does not include the function table. Works great as a class work or homework assignment ...

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Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Graphing Quadratic Functions in Vertex Form. Save Copy. Log InorSign Up. f x = a x − h 2 + k. 1. a = 1. 2. h = 0. 3. k = 0. 4. 5 key points. 5. slope between vertex and first point (click folder to show) ...

Graphing Quadratics in Vertex Form New Years Worksheet & Coloring Activity Graphing Quadratics in Vertex Form Cut and Paste Activity Graphing Quadratics Activity Bundle Graphs of Quadratic Functions in Vertex Form Activity Cut & Paste Graphing Quadratic Equations in Vertex Form - Group Activity TPT empowers educators to teach at their best.

Vertex Form of a Quadratic Function Worksheet. ... 4. f(x) = 4x 2 + 16x + 5. 5. Write the following quadratic function in vertex form and sketch its graph : f(x) = -x 2 + 2 x + 3. 1. Answer : The parabola above opens up with vertex (2, 1). Vertex form of a quadratic function : ... Sat Math Practice; SAT Math Worksheets; PEMDAS Rule; BODMAS rule ...

Practice Worksheet: Graphing Quadratic Functions in Vertex Form For #1-6, label the axis of symmetry, vertex, yr-intercept, and at least three more points on the graph. l] y = (x — 3)2+0 Axis of Symmetry is Vertex: ( 3 , O ) down? Slope to point one unit from the vertex is X y-intercept: (0, q ) Axis of Symmetr is x= Vertex: ( )

This 8-question algebra 1 worksheet provides students with organized practice graphing quadratics in Vertex Form.Students will first identify the vertex and then complete a table of values in order to graph the parabola. I have also provided an option that does not include the function table.Works great as a class work or homework assignment after using this ★FOLDABLE★ to introduce the ...

1] For any quadratic of the form , the axis of symmetry is always the line __________. 2] If the axis of symmetry of a quadratic is and is on the graph, then the point (____, ____) must also be on the graph. 3] For any quadratic of the form 4] The graph of , the y-intercept is always the same point as the _____________.

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March 29, 2023 by tamble. Practice Worksheet Graphing Quadratics In Vertex Form - This Quadratic Worksheet will help you with quadratic equations. It will help you learn how to solve quadratic equations by using the quadratic formula. This formula is the most efficient way to solve quadratic equations. There are however other methods to solve ...

Course: Algebra (all content) > Unit 9. Lesson 4: Quadratic vertex form. Vertex form introduction. Graphing quadratics: vertex form. Warmup: graphing quadratics in vertex form. Graph quadratics in vertex form. Quadratic word problems (vertex form) Quadratic word problems (vertex form) Math >.