Question

compare the graph to its parent function ( f(x) = x^2 ).

1. ( f(x) = -4x^2 ) ( a = ) ____________

(graph of coordinate plane with x and y axes, grid lines)

Explanation:

Step1: Recall the vertex form of a quadratic function

The vertex form of a quadratic function is \( f(x) = ax^2 + bx + c \), and for the function \( f(x) = -4x^2 \), we can compare it to the general form where \( b = 0 \) and \( c = 0 \). The coefficient of \( x^2 \) is \( a \).

Step2: Identify the value of \( a \)

In the function \( f(x) = -4x^2 \), the coefficient of \( x^2 \) is \( -4 \). So, by comparing with the form \( f(x) = ax^2 \), we can see that \( a = -4 \).

Answer:

\( -4 \)