Algebra 1B Unit 9 - Quadratics

Graphs and Quadratics

100

Does the equation below open up or down?

y=-4x^2+3x-11

Down

200

The axis of symmetry for the equation below.

y=x^2+4x+3

x=-2

300

The vertex for the equation below.

y=3x^2-6x

(1, -3)

400

The solutions to the graphed equation can be found on this axis. 

x-axis

500

Sketch a graph opening up that would have one solution. Your graph should only be the axes and your graph. 

The graph should be all positive except for the vertex, which is on the x-axis.

Solving Quadratics (a=1)

100

0=x^2-4

x=+-2

200

What method of solving the quadratic is this?

x^2-10x+21=0

x^2-10x=-21

x^2-10x+25=-21+25

(x-5)^2=4

x-5=+-2

x=3, 7

Completing the Square

300

Solve the quadratic.

0=x^2+3x-4

x=-4, 1

400

Solve the quadratic.

x^2+23x-50=0

x=-25,2

500

Solve the quadratic.

x^2+5x-336=0

x=-21,16

Solving Quadratics (a≠1)

100

4x^2-16=0

x=+-2

200

9x^2-64=0

x==+-8/3

300

2x^2+8x+6=0

x=-3,-1

400

11x^2-8x+12=0

No real solution

500

3x^2-7x-26=0

x=-2, 13/3

Discriminant

100

Listed below is the quadratic formula for assistance. Give the formula for the discriminant.

(-b+-sqrt(b^2-4ac))/(2a)

b^2-4ac

200

If the discriminant is positive, then there are this many solutions.

2

300

How many solutions does this equation have?

x^2-8x+16=0

1

400

If the discriminant is 0, there are this many real solutions.

1

500

How many solutions does this equation have?

3/4x^2-6x+17/12

2

Quadratics Word Problems

100

In real world scenarios, we can model free-falling objects with parabolas and quadratics. Which way will the parabolas open?

Down

200

A pitcher throws a ball in the air. The ball is modelled by the equation given below, where x is the time, in seconds, and y is the height, in feet. When is the ball at its peak?

y=-16x^2+96x+6

3 seconds.

300

A pitcher throws a ball in the air. The ball is modelled by the equation given below, where x is the time, in seconds, and y is the height, in feet. What is the highest point that the ball reaches?

y=-16x^2+96x+6

150 ft

400

A pitcher throws a ball in the air. The ball is modelled by the equation given below, where x is the time, in seconds, and y is the height, in feet. Does the ball fly higher than 100 feet?

y=-16x^2+96x+6

Yes, it does, because the discriminant is positive.

500

A pitcher throws a ball in the air. The ball is modelled by the equation given below, where x is the time, in seconds, and y is the height, in feet. How long is the ball in the air? (Round to the nearest tenth of a second)

y=-16x^2+96x+6

6.1 seconds