Quadratic Function

Question

Find a formula for the quadratic function whose graph has a vertex at (-7,-3) and contains the point (-3, -7)

Answer 1

A quadratic function in vertex form is

 

y = a(x - h)² + k

 

where:

a is the coefficient of the x² term

The vertex is the coordinate (h, k)

 

Since we know our vertex, the function so far is

 

y = a(x + 7)² - 3

 

 

Now we plug in the values of the coordinate (-3, -7) into this form of the equation to find the value of a.

 

-7 = a(-3 + 7)² - 3

 

-7 = 4²a - 3

 

-7 = 16a - 3

 

-4 = 16a

 

-1/4 = a

 

 

Plug in this value of a into the function.

 

y = - (1/4)(x + 7)² - 3

 

 

Now expand.

 

y = - (1/4)(x² + 14x + 49) - 3

 

y = - (1/4)x² - (14/4)x - (61/4)

 

y = - (1/4)(x² + 14x + 61)