This lesson will act as a summary of all the previous lessons in this unit for how to determine the y-value and the x-values/roots of quadratic equations using the various different methods.

We can determine the roots of a quadratic equation using the given formula:

$$x = \cfrac{-\textcolor{green}{b} +- \sqrt{\textcolor{green}{b}^2 - 4\textcolor{red}{a}\textcolor{blue}{c}}}{2\textcolor{red}{a}}$$

This formula is useful for determining the zeroes of a parabola or when it's difficult to factor a quadratic equation. Remember to set the equation to 0 before determining the values of $$\textcolor{red}{a},\textcolor{green}{b},$$ and $$\textcolor{blue}{c}$$.

Determine the y-intercept and x-intercepts of $$2c² + 7c = 4$$ using the quadratic formula. Then, graph the correpsonding parabola based on these intercepts.

## Standard Form

The Standard Form of a quadratic equation is expressed as such:

$$y = ax² + bx + c$$

In order to determine the x-intercepts, we need to fully factor the equation or use the Quadratic Equation. In order to determine the y-intercept, we need to set $$x = 0$$ and solve for $$y$$.

Determine the y-intercept and x-intercepts of $$y = 3x² - 12x + 9$$. Then, graph the correpsonding parabola based on these intercepts.

## Factored Form

The Factored Form of a quadratic equation is expressed as such:

$$y = a(x - p)(x - q)$$

The x-intercepts are $$p$$ and $$q$$ which will make the equation equal $$0$$. The y-intercept can be determined by setting $$x = 0$$, then solving for $$y$$.

Determine the y-intercept and x-intercepts of $$y = -\cfrac{1}{2}(x-3)(x-7)$$. Then, graph the correpsonding parabola based on these intercepts.

## Vertex Form

The Vertex Form of a quadratic equation is expressed as such:

$$y = a(x - h)² + k$$

The vertex is already provided with $$h$$ representing the x-coordinate and $$k$$ representing the y-coordinate. The y-intercept can be determined by setting $$x = 0$$. Depending on the equation, there may be 0, 1 or 2 x-intercepts.

Determine the y-intercept and x-intercepts of $$y = -2(x + 4)² + 3$$. Then, graph the corresponding parabola based on these intercepts.