Lesson 2: Solving Quadratic Equations by Graphing

Property

To find the x-intercepts of a parabola with equation $y = ax^2 + bx + c$:

• Set $y = 0$ and solve the quadratic equation $ax^2 + bx + c = 0$.
• The number of x-intercepts is determined by the discriminant $b^2 - 4ac$:
• If $b^2 - 4ac > 0$: two x-intercepts
• If $b^2 - 4ac = 0$: one x-intercept - If $b^2 - 4ac < 0$: no x-intercepts

Examples

Property

To find the $x$-intercepts of the graph of

we set $y = 0$ and solve the equation

Property

Zero of a Quadratic Function

For any quadratic function $f(x) = ax^2 + bx + c$, if $f(x) = 0$, then $x$ is a zero of the function.
When we find the values of $x$ for which $f(x) = 0$, we are finding the zeros of the quadratic function. When $f(x) = 0$, the point $(x, 0)$ is a point on the parabola, which is an $x$-intercept.