Question
Introduction to Quadratic Functions: End-of-Unit Assessment 1. The function \( f \) is given by \( f(x)=x^{2}+4 x \). Which statement is true of \( f \) Function in A. The graph has a \( f \) intercept at \( (0,-4) \) Function in
Ask by Campos Reed. in the United States
Nov 24,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The \( f \)-intercept is at \( (0, 0) \), not \( (0, -4) \).
Solution
To determine the \( f \)-intercept of the function \( f(x) = x^2 + 4x \), we need to evaluate the function at \( x = 0 \).
Calculating \( f(0) \):
\[
f(0) = 0^2 + 4(0) = 0 + 0 = 0
\]
Thus, the \( f \)-intercept is at the point \( (0, 0) \), not \( (0, -4) \).
Therefore, the statement "The graph has a \( f \) intercept at \( (0, -4) \)" is **false**.
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Simplify this solution The Deep Dive
To find the y-intercept of the function \( f(x) = x^2 + 4x \), simply substitute \( x = 0 \) into the function. This gives \( f(0) = 0^2 + 4(0) = 0 \). Therefore, the correct y-intercept is actually at \( (0, 0) \), not \( (0, -4) \). Also, consider the vertex of the quadratic function. You can find the vertex using the formula \( x = -\frac{b}{2a} \), where \( a = 1 \) and \( b = 4 \). Plugging in these values, you’ll find the x-coordinate of the vertex and then can calculate the corresponding y-value to see where the graph peaks. It’s a handy method for understanding parabolas!
