Question

determine the quadratic function of the form ( f(x) = a(x - h)^2 + k ) whose graph is given on the right

( f(x) = square )
(do not simplify)

Explanation:

Step1: Identify vertex (h,k)

The vertex of the parabola is (2,4), so \( h = 2 \), \( k = 4 \). The function is \( f(x)=a(x - 2)^2+4 \).

Step2: Use point (0, -12) to find a

Substitute \( x = 0 \), \( f(x)=-12 \) into the function:
\( -12=a(0 - 2)^2+4 \)
\( -12 = 4a+4 \)
Subtract 4: \( -16 = 4a \)
Divide by 4: \( a=-4 \)

Step3: Write the function

Substitute \( a=-4 \), \( h = 2 \), \( k = 4 \) into \( f(x)=a(x - h)^2+k \):
\( f(x)=-4(x - 2)^2+4 \)

Answer:

\( -4(x - 2)^2 + 4 \)