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Algebra 1

9.9.3 Vertex Form Given a Vertex and Point

Algebra 19.9.3 Vertex Form Given a Vertex and Point

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Activity

For questions 1 - 2, write an equation in vertex form of the quadratic function that has a vertex at (5, 8) and also goes through the point (3,6)(3,6).

1.

Find the value of aa for vertex form.

2.

Write the equation in vertex form.

For questions 3 and 4, write an equation in vertex form of the quadratic function that has a vertex at (4,3)(4,3) and also goes through the point (2,5)(2,5).

3.

Find the value of aa for vertex form.

4.

Write the equation in vertex form.

For questions 5 - 6, write an equation in vertex form of the quadratic function that has a vertex at (6,2)(6,2) and also goes through the point (3,1)(3,1).

5.

Find the value of aa for vertex form.

6.

Write the equation in vertex form.

Video: Writing an Quadratic Equation from a Vertex and a Point

Watch the following video to learn more about writing a quadratic equation from a vertex and a point.

Self Check

Which of the following is the quadratic equation of the quadratic with a vertex of ( 4 , 2 ) that also goes through the point ( 6 , 5 ) ?
  1. y = 4 7 ( x 6 ) 2 5
  2. y = 7 4 ( x 6 ) 2 5
  3. y = 7 4 ( x 4 ) 2 2
  4. y = 4 7 ( x 4 ) 2 2

Additional Resources

Creating Vertex Form from a Vertex and a Point

Write the quadratic in vertex form that has a vertex at (3,4)(3,4) and goes through the point (1,2)(1,2).

First start with the vertex form of a quadratic function.

y=a(xh)2+ky=a(xh)2+k

Step 1 - Substitute the vertex in at (h,k)(h,k).

y=a(x3)2+4y=a(x3)2+4

Step 2 - Substitute the other point at (x,y)(x,y).

2=a(13)2+42=a(13)2+4

Step 3 - Solve for aa.

2=a(13)2+42=a(13)2+4

2=a(2)2+42=a(2)2+4

2=a(4)+42=a(4)+4

24=a(4)+4424=a(4)+44

2=a(4)2=a(4)

24=a(4)424=a(4)4

a=12a=12

Step 4 - Substitute the value of aa value and the vertex (h,k)(h,k) into the vertex form.

y=12(x3)2+4y=12(x3)2+4

Try it

Try It: Creating Vertex Form from a Vertex and a Point

Write the quadratic in vertex form that has a vertex at (2,5)(2,5) and goes through the point (3,7)(3,7).

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