Question

Problem # 4Which statements regarding the function #(a) = -312 + 187 - 21 are true?Select all that apply.A. When written in vertex form, f(2) =-3(2 - 3)? + 6.B. When written in vertex form, F(a) =-3(2-3)?-2.EC. When written in vertex form, f(z) = (2 - 3)? +6.D. When written in vertex form, f(x)=(2-3-2.E. The vertex of f(I) is located at (3,6).

Answer 1

Given function:

$f(x)\text{ = -3x}^2\text{ + 18x - 21}$

Given the general form of a quadratic equation:

$f(x)\text{ = ax}^2\text{ + bx + c}$

The vertex form of the quadratic equation is:

$\begin{gathered} f(x)\text{ = a\lparen x- h\rparen}^2\text{ + k} \\ Where\text{ h = -}\frac{b}{2a} \\ k\text{ = f\lparen h\rparen} \end{gathered}$

Let us proceed to find the vertex of the quadratic equation:

We have

a = -3, b = 18, c = -21

The x-coordinate of the vertex:

$\begin{gathered} h\text{ = - }\frac{18}{2\times-3} \\ =\text{ 3} \end{gathered}$

The y-coordinate of the vertex:

$\begin{gathered} k\text{ = -3\lparen3\rparen}^2\text{ + 18\lparen3\rparen -21} \\ =\text{ 6} \end{gathered}$

Hence, the vertex of the equation is at (3, 6)

The equation in vertex form is thus:

$f(x)\text{ = -3\lparen x-3\rparen}^2\text{ + 6}$

Answer:

The statements that are correct are:

Option A and option E