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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

9.9.3 Vertex Form Given a Vertex and Point

9.9.3 • Vertex Form Given a Vertex and Point

Access the Desmos guide PDF for tips on solving problems with the Desmos graphing calculator.

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.

9 9 3 Worked Solution FINAL

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(x−h)2+ky=a(x−h)2+k

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

y=a(x−3)2+4y=a(x−3)2+4

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

2=a(1−3)2+42=a(1−3)2+4

Step 3 - Solve for aa.

2=a(1−3)2+42=a(1−3)2+4

2=a(−2)2+42=a(−2)2+4

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

2−4=a(4)+4−42−4=a(4)+4−4

−2=a(4)−2=a(4)

−24=a(4)4−24=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(x−3)2+4y=−12(x−3)2+4

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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