Download presentation

Presentation is loading. Please wait.

Published byDawson Kale Modified over 2 years ago

1
**Objectives Find the zeros of a quadratic function from its graph.**

Find the axis of symmetry and the vertex of a parabola.

2
**Recall that an x-intercept of a function is a value of x when y = 0**

Recall that an x-intercept of a function is a value of x when y = 0. A zero of a function is an x-value that makes the function equal to 0. So a zero of a function is the same as an x-intercept of a function. Since a graph intersects the x-axis at the point or points containing an x-intercept, these intersections are also at the zeros of the function. A quadratic function may have one, two, or no zeros.

3
**Example 1A: Finding Zeros of Quadratic Functions From Graphs**

Find the zeros of the quadratic function from its graph. Check your answer. y = x2 – 2x – 3 y = (–1)2 – 2(–1) – 3 = – 3 = 0 y = 32 –2(3) – 3 = 9 – 6 – 3 = 0 y = x2 – 2x – 3 Check The zeros appear to be –1 and 3.

4
**Example 1B: Finding Zeros of Quadratic Functions From Graphs**

Find the zeros of the quadratic function from its graph. Check your answer. y = x2 + 8x + 16 Check y = x2 + 8x + 16 y = (–4)2 + 8(–4) + 16 = 16 – = 0 The zero appears to be –4.

5
**Example 1C: Finding Zeros of Quadratic Functions From Graphs**

Find the zeros of the quadratic function from its graph. Check your answer. y = –2x2 – 2 The graph does not cross the x-axis, so there are no zeros of this function.

7
**Find the axis of symmetry of each parabola.**

(–1, 0) Identify the x-coordinate of the vertex. The axis of symmetry is x = –1. B. Find the average of the zeros. The axis of symmetry is x = 2.5.

8
Y= x2 + 4x - 21 Check Graph the related quadratic function. The zeros of the related function should be the same as the solutions from factoring. ● The graph of y = x2 + 4x – 21 shows that two zeros appear to be –7 and 3, the same as the solutions from factoring.

9
**Check Graph the related quadratic function.**

Y= x2 – 12x + 36 Check Graph the related quadratic function. ● The graph of y = x2 – 12x + 36 shows that one zero appears to be 6, the same as the solution from factoring.

10
Y=x2 + 4x - 5 Check Graph the related quadratic function. The zeros of the related function should be the same as the solutions from factoring. ● The graph of y = x2 + 4x – 5 shows that the two zeros appear to be 1 and –5, the same as the solutions from factoring.

Similar presentations

Presentation is loading. Please wait....

OK

5.1 Modeling Data with Quadratic Functions

5.1 Modeling Data with Quadratic Functions

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on social media analytics Lecture ppt on computer graphics Ppt on crop production management Ppt on mind controlled wheelchair Ppt on information technology act 2000 Ppt online open port Sample ppt on personality test Ppt on online library management system Ppt online open school Ppt on chapter 3 atoms and molecules