Chapter 11: TRY IT : : 9.91 (page 1069)

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

Short Answer

Expert verified

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) .

$f (x) = {3 x}^{2} + 4 x + 4 f (0) = {3 (0)}^{2} + 4 (0) + 4 f (0) = 4$

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 .

$f (x) = {3 x}^{2} + 4 x + 4 0 = {3 x}^{2} + 4 x + 4$

Solve by using quadratic formula:

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

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

equation. Hence there are no x-intercept points.

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

Short Answer

Step by step solution

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

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

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Find the intercepts of the parabola whose function is f(x)=3x2+4x+4.

Short Answer

Step by step solution

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Discrete Mathematics

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

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