Chapter 13: Q. 2 (page 870)

Graph $f (x) = x^{2} + 4 x - 5$ , by determining whether the graph opens up or down and by finding the vertex, axis of symmetry, and intercepts.

Short Answer

Expert verified

The graph of the function is:

Step by step solution

Step 1. Given information.

The function to be plotted is:

$f (x) = x^{2} + 4 x - 5$

The sign of $x^{2}$ is positive, so graph will open upward.

Step 2. To find x-intercept and y-intercept of the function.

The function can be written as:

$y = x^{2} + 4 x - 5$

$y = x^{2} + 2.2 x + 2^{2} - 2^{2} - 5 y = {(x + 2)}^{2} - 4 - 5 y = {(x + 2)}^{2} - 9$

To find x-intercept:

${(x + 2)}^{2} - 9 = 0 {(x + 2)}^{2} - 3^{2} = 0 (x + 2 - 3) (x + 2 + 3) = 0 (x - 1) (x + 5) = 0 x - 1 = 0 x = 1 x + 5 = 0 x = - 5$

$x -$ intercepts are (1,0) and (-5,0)

To find y-intercept put $x = 0$ in the function.

localid="1647701094732" $y = {(0 + 2)}^{2} - 9 y = 4 - 9 y = - 5$

y-intercept is (0,-5)

Step 3. To find vertex and axis of symmetry of the graph.

The equation of the parabola:

{(x + 2)}^{2} = (y + 9) (x - (- 2)) = 4 . \frac{1}{4} (y - (- 9))

By comparing the equation with standard form of parabola: ${(x - h)}^{2} = 4 a (y - k)$ , where $(h, k)$ is vertex of the parabola.

We get $(h, k) = (- 2, - 9)$

Vertex is: (-2,-9)

The axis of symmetry is:

localid="1647700708833" $x + 2 = 0 x = - 2$

Step 4. To draw the graph of the function.

The graph of the given function can be drawn as:

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Graph $f (x) = x^{2} + 4 x - 5$ , by determining whether the graph opens up or down and by finding the vertex, axis of symmetry, and intercepts.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find x-intercept and y-intercept of the function.

Step 3. To find vertex and axis of symmetry of the graph.

Step 4. To draw the graph of the function.

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Graph f(x)=x2+4x-5, by determining whether the graph opens up or down and by finding the vertex, axis of symmetry, and intercepts.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find x-intercept and y-intercept of the function.

Step 3. To find vertex and axis of symmetry of the graph.

Step 4. To draw the graph of the function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Decision Maths

Probability and Statistics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Graph $f (x) = x^{2} + 4 x - 5$ , by determining whether the graph opens up or down and by finding the vertex, axis of symmetry, and intercepts.