Using quadratic function concepts, it is found that Abby made a mistake on the coordinates of the vertex, which are (-4,1).
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- A quadratic function is defined by:
[tex]y(x) = ax^2 + bx + c[/tex]
- The y-intercept is given by point: [tex](0, y(0))[/tex]
- The vertex is given by: [tex](-\frac{b}{2a}, y(-\frac{b}{2a}))[/tex].
- The axis of symmetry is: [tex]x = -\frac{b}{2a}[/tex]
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The function given is:
[tex]f(x) = -x^2 - 8x - 15[/tex]
- Which is a quadratic equation with: [tex]a = -1, b = -8, c = -15[/tex].
- [tex]f(0) = -0^2 - 8(0) - 15 = -15[/tex], thus, the y-intercept is (0, -15).
[tex]x_v = -\frac{b}{2a} = -\frac{(-8)}{2(-1)} = \frac{8}{-2} = -4[/tex]
- Thus, the x-coordinate of the vertex is x = -4, which is the same as the axis of symmetry.
[tex]f(-4) = -(-4)^2 - 8(-4) - 15 = 1[/tex]
- The vertex is given by: (-4,1).
A similar problem is given at https://brainly.com/question/14680175
