Download presentation

1
**Solving Quadratic Equations by Graphing**

Section 9 – 2

2
**Main Ideas Solve quadratic equations by graphing.**

Estimate solutions of quadratic equations by graphing.

3
**Quadratic Equation: an equation of the form ax2 + bx + c = 0 **

Vocabulary Quadratic Equation: an equation of the form ax2 + bx + c = 0 ,where a ≠ 0.

4
Vocabulary The solutions of a quadratic equation are called the____________________. The roots of a quadratic equation can be found by graphing the related quadratic function f(x) = ax2 + bx + c and finding the _____________________________.

5
d.) Graph y = x2 + 4x + 3 X Y -4 3 -3 -2 -1 Vertex

6
**f.) Solve x2 + 4x + 3 = 0 by graphing**

To solve you need to know where the value of f(x) = 0. This occurs at the x-intercepts, (-3,0) and (-1,0). The solutions are x = {-3, -1}

7
d.) Graph x2 + 7x + 12 = 0 X Y -5 2 -4 -3.5 -0.25 -3 -2 Vertex

8
**f.) Solve x2 + 7x + 12 = 0 by graphing**

To solve you need to know where the value of f(x) = 0. This occurs at the x-intercepts, (-3,0) and (-4,0). The solutions are x = {-4, -3}

9
d.) Graph x2 – 4x + 5 = 0 X Y 5 1 2 3 4 Vertex

10
**f.) Solve x2 – 4x + 5 = 0 by graphing**

To solve you need to know where the value of f(x) = 0. There is no x- intercepts, so there is no real roots Solution: {Ø}

11
d.) Graph x2 – 6x + 9 = 0 X Y 1 4 2 3 5 Vertex

12
**f.) Solve x2 – 6x + 9 = 0 by graphing**

To solve you need to know where the value of f(x) = 0. This occurs at the x-intercepts (3,0). Solution: {3}

13
**Solving Quadratic Equations by Graphing**

Section 9 – 2 Day 2

14
**Main Ideas Solve quadratic equations by graphing.**

Estimate solutions of quadratic equations by graphing.

15
Estimate Solutions The roots of a quadratic equation may not be integers. If exact roots cannot be found, they can be estimated by finding the consecutive integers between which the roots lie.

16
**Example 2: Solve the equation by graphing**

x2 + 6x + 6 = 0 a.) Write the equation of the axis of symmetry b.) Find the coordinates of the vertex of the graph of each function. c.) Identify the vertex as a maximum or a minimum. d.) Then graph the function. e.) State the Domain and Range f.) Determine what the x-intercept or zeros are to solve the quadratic equation.

17
**Solve x2 + 6x + 6 = 0 by graphing**

a.) equation of axis of symmetry a = _____ b = ____ c = ____ b.) Find the vertex. 1 6 6 y = x2 + 6x + 6 when x = -3 y = (-3)2 + 6(-3) + 6 y = y = -3 Vertex (-3, -3)

18
**Solve x2 + 6x + 6 = 0 by graphing**

c.) Identify the vertex as a maximum or a minimum. Since the coefficient of the x2-term is positive, the parabola opens upward, and the vertex is a minimum point.

19
d.) Graph x2 + 6x + 6 = 0 X Y -5 1 -4 -2 -3 -1 Vertex

20
**Domain: D: {x I x is all real numbers.} Range: R: {y I y ≥ -3} **

e.) Graph x2 + 6x + 6 = 0 Domain: D: {x I x is all real numbers.} Range: R: {y I y ≥ -3}

21
**f.) Solve x2 + 6x + 6 = 0 by graphing**

The x-intercepts of the graph are between -5 and -4 and between -2 and -1. So one root is between 5 and 4, and the other root is between 2 and 1. -5 < x < -4 -2 < x < -1

22
**Try 4: Solve the equation by graphing**

x2 – 2x – 4 = 0 a.) Write the equation of the axis of symmetry b.) Find the coordinates of the vertex of the graph of each function. c.) Identify the vertex as a maximum or a minimum. d.) Then graph the function. e.) Determine what the x-intercept or zeros are to solve the quadratic equation.

23
**Solve x2 – 2x – 4 = 0 by graphing**

a.) equation of axis of symmetry a = ____ b = ____ c = ____ b.) Find the vertex. 1 -2 -4 y = x2 – 2x – 4 when x = 1 y = (1)2 + -2(1) + -4 y = y = -5 Vertex (1, -5)

24
**Solve x2 – 2x – 4 = 0 by graphing**

c.) Identify the vertex as a maximum or a minimum. Since the coefficient of the x2-term is positive, the parabola opens upward, and the vertex is a minimum point.

25
d.) Graph x2 – 2x – 4 = 0 X Y -1 -4 1 -5 2 3 Vertex

26
e.) Domain and Range Domain: D: {x I x is all real numbers.} Range: R: {y I y ≥ -5}

27
**Solve x2 + 6x + 6 = 0 by graphing**

The x-intercepts of the graph are between -2 and -1 and between 3 and 4. So one root is between - 2 and -1, and the other root is between 3 and 4. -2 < x < -1 3 < x < 4

28
**2 roots x = { -4, 3} x – 3 = 0 x + 4 = 0 x + -3 + 3 = 0 + 3**

Use factoring to determine how many times the graph of each function intersects the x-axis. Identify the root. f(x) = x2 + x – 12 0 = x2 + x – 12 0 = (x – 3)(x + 4) x – 3 = 0 x = 0 + 3 x = 3 x + 4 = 0 x = x = - 4 2 roots x = { -4, 3}

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google