Chapter 11: Q. 56 (page 1101)

In the following exercises, graph each equation by using properties.
$y = 8 x^{2} - 10 x + 3$

Short Answer

Expert verified

On graphing the equation we get,

Step by step solution

Step 1. Given information.

Consider the given function,

$y = 8 x^{2} - 10 x + 3$

Compare $y = a x^{2} + b x + c$ with the given function,

$a = 8, b = - 10, c = 3$

Since $a = 8$ , the parabola opens to the right.

The axis of symmetry, $x = - \frac{b}{2 a}$ . Then,

$x = - \frac{(- 10)}{2 (8)} = \frac{5}{8}$

Step 2. Find the vertex.

The vertex is on the line $x = \frac{5}{8}$ .

Substitute $x = \frac{5}{8}$ in the original equation,

$y = 8 {(\frac{5}{8})}^{2} - 10 (\frac{5}{8}) + 3 = \frac{25}{8} - \frac{25}{4} + 3 = - \frac{1}{8}$

Therefore, the vertex is $(\frac{5}{8}, - \frac{1}{8})$ .

Substitute $y = 0$ in the original equation,

$0 = 8 x^{2} - 10 x + 3 x = \frac{3}{4}, \frac{1}{2}$

Therefore, the x-intercepts are $(\frac{3}{4}, 0), (\frac{1}{2}, 0)$ .

Step 3. Find the y-intercept.

Substitute $x = 0$ in the original equation,

$y = 8 {(0)}^{2} - 10 (0) + 3 y = 3$

Therefore, the y-intercept is $(0, 3)$ .

The point symmetric to localid="1645199207623" $(0, 3)$ across the axis of symmetry is $(\frac{5}{4}, 3)$ .

On graphing the parabola we get,

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In the following exercises, graph each equation by using properties.
$y = 8 x^{2} - 10 x + 3$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the vertex.

Step 3. Find the y-intercept.

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In the following exercises, graph each equation by using properties.y=8x2-10x+3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the vertex.

Step 3. Find the y-intercept.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Geometry

Applied Mathematics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by using properties.
$y = 8 x^{2} - 10 x + 3$