help **12. Graph the following quadratic function using its properties.**\[ G(x) = -x^2 + 2x + 8 \]To graph this quadratic function effectively, we should examine its properties, such as the vertex, axis of symmetry, and intercepts.- **Vertex**: The vertex can be found using the formula \( x = -\frac{b}{2a} \). For the function \( G(x) = -x^2 + 2x + 8 \), \( a = -1 \) and \( b = 2 \). Solving this gives \( x = -\frac{2}{2(-1)} = 1 \). Substitute back to find \( G(1) = -(1)^2 + 2(1) + 8 = 9 \). Thus, the vertex is at \( (1, 9) \).- **Axis of Symmetry**: This is the vertical line \( x = 1 \).- **Intercepts**: The y-intercept is found by evaluating \( G(x) \) at \( x = 0 \): \( G(0) = 8 \). To find the x-intercepts, set \( G(x) \) to zero and solve for \( x \): \[ 0 = -x^2 + 2x + 8 \] Solving this quadratic equation gives the points of intersection with the x-axis.- **Direction**: Since the coefficient of \( x^2 \) is negative, the parabola opens downwards.By utilizing these properties, the graph of the function can be accurately depicted.

Name: help **12. Graph the following quadratic function using its properties
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: help **12. Graph the following quadratic function using its properties.**\[ G(x) = -x^2 + 2x + 8 \]To graph this quadratic function effectively, we should examine its properties, such as the vertex, axis of symmetry, and intercepts.- **Vertex**: The