Question

Given the quadratic function

F(x)=3x^2-24x+49

A. Use “completing the squares” to convert the quadratic function into vertex form

B. State the vertex

C. Find the x and y intercepts

D. Graph the function

Answer 1

See below.

Explanation:

A. F(x)=3x^2 - 24x + 49

f(x) = 3(x^2 - 8x) + 49

f(x) = 3 [(x - 4)^2 - 16] + 49

f(x) = 3(x - 4)^2 - 48 + 49

f(x) = 3(x - 4)^2 + 1 <------- Vertex form. (answer).

B.

The vertex is at (4, 1). (answer).

C.

The y-intercept occurs when x = 0:

y = 3(0- 4)^2 + 1

= 3*16 + 1

= 49

The y-intercept is at (0, 49). (answer)

The x intercepts occur when y = 0:

3(x - 4)^2 + 1 = 0

3(x - 4)^2 = -1

(x - 4)^2 = -1/3

Since there is no real square root of a negative there are no x-intercepts.

(Answer)