Name:__________ warm-up 4-8 Write y = 2x 2 - 12x + 44 in vertex formIdentify the vertex of y = 5x 2 + 30x + 44. Find the axis of symmetry of y = 5x 2 +

Name:__________ warm-up 4-8

Write y = 2x

2 - 12x + 44 in vertex form Identify the vertex of y = 5x

2 + 30x + 44.

Find the axis of symmetry of y = 5x

2 + 30x + 44.Find the axis of symmetry of y = 5x

2 + 30x + 44.

What is the direction of the opening of the graph of y = 5x

2 + 30x + 44?

Graph the quadratic function y = 5x

2 + 30x + 44.

The graph of y = x

2 is reflected in the x-axis and shifted left three units. Which of the following equations represents the resulting parabola?

A. y = (x – 3)2

B. y = –(x – 3)2

C. y = –(x + 3)2

D. y = –x

2 + 3

A.

C.

B.

D.

Name:__________ warm-up Review

Write y = y = 2x

2 - 12x + 25 in vertex form Identify the vertex of y = 2x

2 - 12x + 25.

Find the axis of symmetry of y = 2x

2 - 12x + 25.Find the axis of symmetry of y = 2x

2 - 12x + 25.

What is the direction of the opening of the graph of y = 2x

2 - 12x + 25?

Graph the quadratic function y = 2x

2 - 12x + 25

Solve x

2 - 3x -10 ˂ 0 algebraically and then graph.

Details of the DayEQ:How do quadratic relations model real-world problems and their solutions?Depending on the situation, why is one method for solving a quadratic equation more beneficial than another?How do transformations help you to graph all functions?Why do we need another number set?

I will be able to…

Activities:Warm-upReview homework –Notes: 4-8 Quadratic InequalitiesClass work/ HW

Vocabulary:

quadratic inequality

.• Graph quadratic inequalities in

two variables.

• Solve quadratic inequalities in

one variable.

https://www.youtube.com/watch?v=BXWzNp-4ilAhttps://www.youtube.com/watch?v=t54ccHYVhoohttps://www.youtube.com/watch?v=8FCV2-EjgXghttps://www.mathsisfun.com/algebra/inequality-quadratic-solving.html

Details of the DayEQ:How do quadratic relations model real-world problems and their solutions?Depending on the situation, why is one method for solving a quadratic equation more beneficial than another?How do transformations help you to graph all functions?Why do we need another number set?

I will be able to…

Activities:Warm-up- vocabulary self quizReview homework –Round robin student reviewStudent presentations

.• Graph quadratic inequalities in

two variables.

• Solve quadratic inequalities in

one variable.

4-8 Quadratic Inequalities

A Quick Review Write y = 5x

2 + 30x + 44 in vertex form Identify the vertex of y = 5x

2 + 30x + 44.

Find the axis of symmetry of y = 5x

2 + 30x + 44.Find the axis of symmetry of y = 5x

2 + 30x + 44.

A Quick Review What is the direction of the opening of the graph of y = 5x

2 + 30x + 44?

Graph the quadratic function y = 5x

2 + 30x + 44.

The graph of y = x

2 is reflected in the x-axis and shifted left three units. Which of the following equations represents the resulting parabola?

A. y = (x – 3)2

B. y = –(x – 3)2

C. y = –(x + 3)2

D. y = –x

2 + 3

A.

C.

B.

D.

Notes and examplesGraph the related quadratic equation, y = x2 – 3x + 2. Since the inequality symbol is >, the parabola should be dashed.

Test a point inside the parabola, such as (1, 2). Shade the region

Notes and examplesgraph of y < –x2 + 4x + 2

Notes and examplesSolve x

2 – 4x + 3 < 0 by graphing.

The solution consists of the x-values for which the graph of the related quadratic function lies below the x-axis. Begin by finding the roots of the related equation.

Related

Factor

Zero Product Property

Solve each equation

Notes and examplesSketch the graph of the parabola that has x-intercepts at 3 and 1. The graph should open up since a > 0. The graph lies below the x-axis to the right of x = 1 and to the left of x = 3.

Notes and examplesWhat is the solution to the inequality x

2 + 5x + 6 < 0?

Notes and examplesSolve 0 ≤ –2x2 – 6x + 1 by graphing

This inequality can be rewritten as –2x2 – 6x + 1 ≥ 0. The solution consists of the x-values for which the graph of the related quadratic equation lies on and above the x-axis. Begin by finding roots of the related equation

Sketch the graph of the parabola

Write Equation

Write quadratic equation

Substitute

Simplify

Notes and examplesTest one value of x less than –3.16, one between –3.16 and 0.16, and one greater than 0.16 in the original inequality.

Notes and examplesSolve 2x2 + 3x – 7 ≥ 0 by graphing.

A. {x | –2.77 ≤ x ≤ 1.27}

B. {x | –1.27 ≤ x ≤ 2.77}

C. {x | x ≤ –2.77 or x ≥ 1.27}

D. {x | x ≤ –1.27 or x ≥ 2.77}

Notes and examplesThe height of a ball above the ground after it is thrown upwards at 28 feet per second can be modeled by the function h(x) = 28x – 16x

2, where the height h(x) is given in feet and the time x is in seconds. At what time in its flight is the ball within 10 feet of the ground?h(x)≤15 Original inequality

Graph the related function using a graphing calculator.

Notes and examplesThe height of a ball above the ground after it is thrown upwards at 28 feet per second can be modeled by the function h(x) = 28x – 16x

2, where the height h(x) is given in feet and the time x is in seconds. At what time in its flight is the ball within 10 feet of the ground?

A. for the first 0.5 second and again after 1.25 seconds

B. for the first 0.5 second only

C. between 0.5 second and 1.25 seconds

D. It is never within 10 feet of the ground.

Notes and examplesSolve x2 + x ≤ 2 algebraicallyFirst, solve the related quadratic equation x2 + x = 2.

Test a value in each interval to see if it satisfies the original inequality

Plot points on a number line. Use closed circles since these solutions are included. Notice that the number line is separated into 3 interval

Notes and examplesSolve x2 + 5x ≤ –6 algebraically. What is the solution?