Question

which is $f(6)$ for the quadratic function graphed? options: -2, -0.5, 1.5, 4

Explanation:

Step1: Identify vertex of parabola

The vertex (minimum point) is at $(1, -3)$.

Step2: Write vertex form of quadratic

Vertex form: $f(x)=a(x-h)^2+k$, where $(h,k)=(1,-3)$
$f(x)=a(x-1)^2-3$

Step3: Solve for $a$ using a point

Use point $(0, -2)$:
$-2=a(0-1)^2-3$
$-2=a(1)-3$
$a=-2+3=1$
So $f(x)=(x-1)^2-3$

Step4: Calculate $f(6)$

Substitute $x=6$:
$f(6)=(6-1)^2-3=5^2-3=25-3$

Answer:

4