Question

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

Explanation:

Step1: Identify vertex of parabola

The vertex (minimum point) is at $(1, -3)$. The vertex form of a quadratic is $y = a(x-h)^2 + k$, so substitute $h=1, k=-3$:
$y = a(x-1)^2 - 3$

Step2: Solve for $a$ using a point

Use the point $(0, -2)$ on the graph:
$-2 = a(0-1)^2 - 3$
$-2 = a(1) - 3$
$a = -2 + 3 = 1$
So the function is $y = (x-1)^2 - 3$

Step3: Calculate $f(6)$

Substitute $x=6$ into the function:
$y = (6-1)^2 - 3 = 5^2 - 3 = 25 - 3$

Answer:

D. 4