Question
In the following exercise, find the coordinates of the vertex for the parabola defined by the given quadratic function.
f left parenthesis x right parenthesis equals negative 4 left parenthesis x plus 8 right parenthesis squared plus 7
Question content area bottom
Part 1
The vertex is
enter your response here. (Type an ordered pair.)
f left parenthesis x right parenthesis equals negative 4 left parenthesis x plus 8 right parenthesis squared plus 7
Question content area bottom
Part 1
The vertex is
enter your response here. (Type an ordered pair.)
Answers
GPT-4o mini
To find the vertex of the parabola defined by the quadratic function \( f(x) = -4(x + 8)^2 + 7 \), we can directly identify the vertex since the function is written in the vertex form \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.
1. In your function, \( a = -4 \), \( h = -8 \) (because it's \( x + 8 \), which is \( x - (-8) \)), and \( k = 7 \).
2. Therefore, the vertex \((h, k)\) is:
\[
(-8, 7)
\]
So the coordinates of the vertex are:
\[
\text{The vertex is } (-8, 7).
\]
1. In your function, \( a = -4 \), \( h = -8 \) (because it's \( x + 8 \), which is \( x - (-8) \)), and \( k = 7 \).
2. Therefore, the vertex \((h, k)\) is:
\[
(-8, 7)
\]
So the coordinates of the vertex are:
\[
\text{The vertex is } (-8, 7).
\]