Answer:
Step-by-step explanation:
The standard form of a quadratic equation is ax² + bx + c, where a ≠ 0.
Given that the axis of symmetry occurs at x = h, then we can assume that the h coordinate of the vertex is the same as the x-coordinate in an ordered pair, (x, y).
In order to find the vertex, (h, k), use the following formula to solve for the value of h:
[tex]h = \frac{-b}{2a}[/tex].
Example:
To demonstrate this concept, let's say that we're given the following quadratic equation: 2x² + 8x + 8, where a = 2, b = 8, and c = 8. Substitute the values of a and b into the given equation for solving the x-coordinate (h) of the vertex:
[tex]h = \frac{-b}{2a}[/tex]
[tex]h = \frac{-8}{2(2)} = \frac{-8}{4} = -2[/tex]
Therefore, h = -2.
Next, substitute the value of h = -2 into the given quadratic equation in order to solve for its corresponding y-coordinate (k ) of the vertex:
k = 2x² + 8x + 8
where: a = 2, b = 8, and c = 8
k = 2(-2)² + 8(-2) + 8
k = 2(4) - 16 + 8
k = 8 - 16 + 8
k = 0
Therefore, the vertex of the quadratic equation, 2x² + 8x + 8 is (-2, 0).
