General Quadratics
Does the quadratic y=4(x-3)2+10 have a maximum or minimum? What is the max/min value?
(20 seconds)
minimum of 10
How does solving quadratic equations, relate to the graph of the parabola?
(20 seconds)
When solving you are finding the x-intercepts
Solve.
0=(2x-5)(x+7)
(45 seconds)
x=-7 and x=5/2
What is the quadratic formula?
(20 seconds)
x=(-b+-sqrt(b^2-4ac))/(2a)
When a question is asking for the maximum/minimum value, what is it asking you to find?
y-value of the vertex
What are the two ways to solve a quadratic equation? (20 seconds)
Factoring and Quadratic Formula
Without solving, determine how many x-intercepts the relation y=-(x-2)2-4 has.
(30 seconds)
none
Solve by factoring.
x2-7x+10=0
(1 minute)
x=5 and x=2
Solve using quadratic formula.
0=3x2+14x+5
(2 minutes)
x=-0.39 and x=-4.28
A ball is thrown upward and models the path h=-4.9t2+8.4t+1.5. where h is the height of the ball, in metres, after t seconds. What height was the ball thrown from?
1.5 m
Which type of factoring do you always look for first?
(20 seconds)
Common factoring.
What does it mean if a quadratic has only one x-intercept?
(30 seconds)
The x-intercept is the vertex
Solve by factoring.
-3=5x2+16x
(1 minute)
x=-3 and x=-1/5
Solve using quadratic formula.
x2-4x+15=0
(2 minutes)
no solutions
A toy rocket is launched and its height is modelled by the equation h=-4.9t2+8.1t+3 where h is the height in metres above the ground, and t is the time in seconds. How long does it take the rocket to hit the ground?
t=1.96 seconds
How many solutions can you get when solving a quadratic equation?
(20 seconds)
0, 1, or 2
Find the x-interecepts and vertex for the function
y= -x2-5x
(2 minutes)
x=0 and x=-5
vertex=(-2.5, 6.25)
Solve by factoring.
2x2=-2x+24
(2 minutes)
x=3 and x=-4
Solve using quadratic formula.
4x2=12-13x
(2 min 30 seconds)
x=3/4 and x=-4
The three sides of a right triangle are consecutive even integers. Write an equation in standard form that you could use to solve for the side lengths. DO NOT SOLVE.
x2-4x-12=0
If x=-5, what is the value of y?
y=4x2+10x-20
(45 seconds)
y=30
A parabola has a vertex (-3,7) and one x-intercept is -11. Find the other x-intercept.
(1 minute)
x=5
Write a quadratic equation with solutions x=-2 and x=3 in the form ax2+bx+c=0
(3 minutes)
x2-x-6
Solve using quadratic formula.
(x+3)2=(2x+5)(2x-5)
(5 minutes)
x=-2.51 and x=4.51
A store sells 3000 Halloween-themed wigs at $20 each every month. For each $1 increase in price, they would sell 100 less wigs. What is the maximum revenue?
$62500