Graphing Quadratic Equations: example 10.47

Find the intercepts of the parabola $y = 5 x^{2} + x + 4$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the intercepts of the parabola $y = 3 x^{2} + 4 x + 4 .$

How did it go?


To find the y-intercept, let $x = 0$ and solve for y.		When $x = 0$ , then $y = 4$ . The y-intercept is the point $(0, 4)$ .

To find the x-intercept, let $y = 0$ and solve for x.
Find the value of the discriminant to predict the number of solutions and so x-intercepts.		$\begin{matrix} \begin{matrix} b^{2} & - & 4 a c \\ 1^{2} & - & 4 \cdot 5 \cdot 4 \\ 1 & - & 80 \end{matrix} \\ −79 \end{matrix}$
Since the value of the discriminant is negative, there is no real solution to the equation.		There are no x-intercepts.


To find the y-intercept, let $x = 0$ and solve for y.		When $x = 0$ , then $y = 4$ . The y-intercept is the point $(0, 4)$ .

To find the x-intercept, let $y = 0$ and solve for x.
Find the value of the discriminant to predict the number of solutions and so x-intercepts.		$\begin{matrix} \begin{matrix} b^{2} & - & 4 a c \\ 1^{2} & - & 4 \cdot 5 \cdot 4 \\ 1 & - & 80 \end{matrix} \\ −79 \end{matrix}$
Since the value of the discriminant is negative, there is no real solution to the equation.		There are no x-intercepts.