Rewrite the quadratic function y = 3x^2 + 24x + 44 in Vertex Form:

Question

A: y = 3(x - 4)^2 + 4

B: y = 1/3(x + 4)^2 - 4

C: y = 3(x - 4)^2 - 4

D: y = 3(x + 4)^2 - 4

E: y = 3(x + 4)^2 + 4

Answer 1

An equation in vertex form is   y=a(x - h)² + k

 

where:

a is the coefficient of the x² term

Vertex has coordinates (h, k).

 

We can find the value of h using this formula:

 

h = -b / 2a

 

where:

a = 3

b = 24

c = 44

 

h = -24 / (2 * 3)

h = -24 / 6

h = -4

 

Next we can find the value of k by evaluating y when x=-4.

 

k = y(h)

 

k = 3(-4)² + 24(-4) + 44

k = 48 - 96 + 44

k = -4

 

So what do we know?

 

a = 3

Vertex is (-4, -4)

 

Plug in these values into the vertex form.

 

y = 3(x + 4)² - 4

 

 

To check, we can expand the vertex form and should get back the original equation.

 

y = 3(x + 4)(x + 4) - 4

 

y = 3(x² + 8x + 16) - 4

 

y = 3x² + 24x + 48 - 4

 

y = 3x² + 24x + 44

 

 

This checks out!