Question

consider the graph of $f(x)$ below.
the equation for $f(x)$ can be written as $f(x) = a(x - h)^2 + k$. what are the values of $a$ and $h$
note: your answers should be integers.
$a = $
$h = -5$

Explanation:

Step1: Identify vertex form parameters

The vertex form of a parabola is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex. From the graph, the vertex is \((-6, -5)\), so \( h = -6 \) and \( k = -5 \).

Step2: Find 'a' using a point

We know the point \((-5, -1)\) lies on the parabola. Substitute \( x = -5 \), \( f(x) = -1 \), \( h = -6 \), and \( k = -5 \) into the vertex form:
\( -1 = a(-5 - (-6))^2 + (-5) \)
Simplify inside the parentheses: \( -5 + 6 = 1 \), so:
\( -1 = a(1)^2 - 5 \)
\( -1 = a - 5 \)

Step3: Solve for 'a'

Add 5 to both sides: \( a = -1 + 5 = 4 \).

Answer:

For \( a \): \( 4 \)
For \( h \): \( -6 \) (Note: The initial wrong value for \( h \) in the image should be corrected to \(-6\) as the vertex is \((-6, -5)\).)