04 - Determining the Equation of a Quadratic Relation in Factored Form PDF

Preview

Summary

Notes...

Description

4 - Determining the Equation of a Quadratic Relation in Factored Form

MPM2D – Introduction to Quadratics

Date: ______________________________________________

Determining the Equation of a Quadratic in Factored Form Example 1 Determine the equation, in factored form, given that the x-intercepts are –2 and 4, and the y-intercept is 5.

Example 2 Determine the equation, in factored form, given that the zeros are –3 and 5, and a point on the graph has coordinates "7,2%.

Example 3 Determine the equation, in factored form, given the following graph.

Page 1 of 4

4 - Determining the Equation of a Quadratic Relation in Factored Form

MPM2D – Introduction to Quadratics

Example 4 Determine the equation, in factored form, given that there is only one zero, which is 2, and the parabola passes through the point "5, −2%.

Example 5 Determine the equation, in factored form, given that the zeros are –1 and 5, and an optimal value of –7.

Page 2 of 4

4 - Determining the Equation of a Quadratic Relation in Factored Form

MPM2D – Introduction to Quadratics

Homework 1. Determine the zeros and optimum values for the following equations. a. ) = "20 − 2,%"30 + 3, % b. ) = "30 − 4, %"16 + 2, % c. ) = "4 − 0.25,%"25 + 2, % d. ) = "200 − 25, %"9 + 3, % e. ) = "40 − 5, %"20 + 5, %

2. A quadratic has the equation ) = 1 ", − 2 %", − 3 %. Find the value of a when: a. ) = 1 ", − 2%", + 6% and "3,5% is a point on the graph. b. the parabola has zeros of 4 and –2 and a y-intercept of 1 c. the parabola has x-intercepts of 4 and –2 and a y-intercept of –1 d. the parabola has zeros of 5 and 0 and a minimum of –10 e. the parabola has x-intercepts of 5 and –3 and a maximum value of 6

3. Determine the equation (in factored form) of the quadratic relationship given: x-intercepts

y-intercept

a.

–2 and 4

5

b.

–5 and –2

–4

c.

3 and 8

–6

4. A parabola has zeros at "5,0% and "−3,0%. It passes through the point "6,18%. a. What is the equation for the axis of symmetry? b. Determine the equation of the parabola. c. What are the coordinates of the vertex? d. Sketch the parabola.

Page 3 of 4

4 - Determining the Equation of a Quadratic Relation in Factored Form

MPM2D – Introduction to Quadratics

Answers 1. Zeros

Optimum Value

a.

10 and –10

600

b.

7.5 and –8

480.5

c.

16 and –12.5

101.5

d.

8 and –3

2268.75

e.

8 and –4

900

2. a. d.

5

7

b. − 8

6 8

e. −

5

c.

7 8

9 8

3. 5

a. ) = − 8 ", − 4 %", + 2%

b. ) = −

: 5

", + 5%", + 2%

c. ) = −

7

4. a. , = 1

b. ) = 2", − 5%", + 3%

Page 4 of 4

c. "1, −32%

;

", − 3 %", − 8%...