Answer:
Let's work through the information for the factored form of the quadratic equation -2(x + 1)(x + 13):
1. Zeros/Roots: The zeros or roots are the values of x that make the quadratic equation equal to zero. To find them, set the equation equal to zero and solve for x:
-2(x + 1)(x + 13) = 0
Set each factor equal to zero and solve for x:
x + 1 = 0 => x = -1
x + 13 = 0 => x = -13
So, the zeros/roots are x = -1 and x = -13.
2. Axis of Symmetry: The axis of symmetry for a quadratic equation in the form y = a(x - h)^2 + k is given by x = h. In the case of your equation, it's already in factored form, so you can determine the axis of symmetry by averaging the zeros:
Axis of symmetry = (-1 - 13) / 2 = -14 / 2 = -7
So, the axis of symmetry is x = -7.
3. Vertex: The vertex of the quadratic equation can be found using the axis of symmetry. Since the axis of symmetry is x = -7, plug this value into the equation to find the corresponding y-value:
-2(-7 + 1)(-7 + 13) = -2(-6)(6) = -72
So, the vertex is (-7, -72).
4. Y-Intercept: The y-intercept occurs when x = 0. Plug x = 0 into the equation:
-2(0 + 1)(0 + 13) = -2(1)(13) = -26
So, the y-intercept is at y = -26.
To summarize:
Zeros/Roots: x = -1 and x = -13.
Axis of Symmetry: x = -7.
Vertex: (-7, -72).
Y-Intercept: y = -26.
Explanation: