Question

Find the intercepts of the parabola whose function is $f\left(x\right)={3x}^2+4x+4.$

Short answer

• The y-intercept at the point (0, 4).
• There are no x-intercepts.

Step-by-step solution

Step 1. To find the y-intercept, let x = 0 andsolve for f (x) .

$$\begin{gathered} f\left(x\right)={3x}^2+4x+4 \\ f\left(0\right)={3\left(0\right)}^2+4\left(0\right)+4 \\ f\left(0\right)=4 \end{gathered}$$

When x = 0 , then f (0) = 4 .

The y-intercept at the point (0, 4) .

Step 2. To find the x-intercept, let f (x) = 0 andsolve for x .

$$\begin{gathered} f\left(x\right)={3x}^2+4x+4 \\ 0={3x}^2+4x+4 \end{gathered}$$

Solve by using quadratic formula:

$$\begin{gathered} a=3,b=4,c=4 \\ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ x=\frac{-\left(4\right)\pm \sqrt{4^2-4\left(3\right)\left(4\right)}}{2\left(3\right)} \\ x=\frac{-4\pm \sqrt{16-48}}{6} \\ x=\frac{-4\pm \sqrt{-32}}{6} \end{gathered}$$

Since the value of the discriminant is negative, there is no real solution to the

equation. Hence there are no x-intercept points.