Question

2. Abby found the axis of symmetry, x-coordinate, the vertex, and y-intercept

Answer 1

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:

$y(x) = ax^2 + bx + c$

• The y-intercept is given by point: $(0, y(0))$
• The vertex is given by: $(-\frac{b}{2a}, y(-\frac{b}{2a}))$.
• The axis of symmetry is: $x = -\frac{b}{2a}$

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The function given is:

$f(x) = -x^2 - 8x - 15$

• Which is a quadratic equation with: $a = -1, b = -8, c = -15$.
• $f(0) = -0^2 - 8(0) - 15 = -15$, thus, the y-intercept is (0, -15).

$x_v = -\frac{b}{2a} = -\frac{(-8)}{2(-1)} = \frac{8}{-2} = -4$

• Thus, the x-coordinate of the vertex is x = -4, which is the same as the axis of symmetry.

$f(-4) = -(-4)^2 - 8(-4) - 15 = 1$

• The vertex is given by: (-4,1).

A similar problem is given at brainly.com/question/14680175