Question

How do you find the vertex of a quadratic equation in standard form?

Answer 1

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:

$h = \frac{-b}{2a}$.

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:

$h = \frac{-b}{2a}$

$h = \frac{-8}{2(2)} = \frac{-8}{4} = -2$

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).

Answer 2

Answer:

Get the equation in the form y = ax2 + bx + c.

Calculate -b / 2a. This is the x-coordinate of the vertex.

To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.