Graph the quadratic function. $$f ( x ) = - 4 x ^ { 2 } + 2$$
C) $\mathrm { d }$.

Question

Quizplus · Accepted Answer

The given quadratic function is in the form $f(x) = ax^2 + b$, where $a = -4$ and $b=2$. Since $a < 0$, the graph of the quadratic function is a downwards facing parabola. The vertex of the parabola is given by $(h,k)$, where $h = -\frac{b}{2a}$ and $k = f(h)$. Substituting the values of $a$ and $b$, we get $h = -\frac{2}{-8} = \frac{1}{4}$ and $k = f\left(\frac{1}{4}\right) = -4 \cdot \left(\frac{1}{4}\right)^2 + 2 = \frac{3}{2}$. Therefore, the vertex is at $\left(\frac{1}{4},\frac{3}{2}\right)$. Since the coefficient of $x^2$ is $-4$, the parabola is relatively narrow. Combine this information and we can deduce that the correct representation is B.

Graph the Quadratic Function f(x)=−4x2+2f ( x ) = - 4 x ^ { 2 } + 2f(x)=−4x2+2

Graph the Quadratic Function $f ( x ) = - 4 x ^ { 2 } + 2$