Question

which equation best matches the graph shown below?
answer
$y = 5(x - 4)^2 + 3$
$y = 5(x + 4)^2 + 3$
$y = 5(x - 4)^2 - 3$
$y = 5(x + 4)^2 - 3$

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

Step2: Identify the vertex from the graph

From the graph, the vertex of the parabola is at \((-4, 3)\). So, \( h=-4 \) and \( k = 3 \).

Step3: Substitute h and k into vertex form

Substituting \( h=-4 \) and \( k = 3 \) into \( y = a(x - h)^2 + k \), we get \( y=a(x - (-4))^2+3=a(x + 4)^2+3 \). The coefficient \( a = 5 \) (as seen in all options), so the equation is \( y = 5(x + 4)^2+3 \).

Answer:

\( y = 5(x + 4)^2+3 \)