Chapter 11: Q. 53 (page 1101)

In the following exercises, graph each equation by using properties.
$y = - x^{2} + 4 x - 3$

Short Answer

Expert verified

The graph is

Step by step solution

Given information

Given the function $y = - x^{2} + 4 x - 3$

State in standard form

Comparing, we get

Identify the constants a,h,k and the other parameters

Comparing, we get

$y = {(x - 2)}^{2} + 1 a = 1 (h, k) = (2, 1)$

As $a = 1$ , the parabola opens to the right

Calculate the y intercept

Calculating, we get

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

Calculate the x intercept

Calculating, we get

$y = - {(x - 2)}^{2} + 1 - {(x - 2)}^{2} + 1 = 0 - {(x - 2)}^{2} = - 1 x - 2 = \pm 1 x = 3, 1$

The axis of symmetry is $x = 2$

Sketching the graph

The graph is

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In the following exercises, graph each equation by using properties.
$y = - x^{2} + 4 x - 3$

Short Answer

Step by step solution

Given information

State in standard form

Identify the constants a,h,k and the other parameters

Calculate the y intercept

Calculate the x intercept

Sketching the graph

One App. One Place for Learning.

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In the following exercises, graph each equation by using properties.y=-x2+4x-3

Short Answer

Step by step solution

Given information

State in standard form

Identify the constants a,h,k and the other parameters

Calculate the y intercept

Calculate the x intercept

Sketching the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Mechanics Maths

Applied Mathematics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by using properties.
$y = - x^{2} + 4 x - 3$