Solving Quadratics
x2 - 1 = 0
{-1, 1}
How many solutions might a quadratic equation have?
0, 1, or 2
When can the completing the square method be used?
Any quadratic equation
What is the quadratic formula?
x = -b +- sqrt(b2 - 4ac) /(2a)
What are three ways you can solve for the x-intercepts?
Completing the Square
Zero Product Property (factoring)
Quadratic Formula
Graphing
Square root method
Solve the following quadratic equation by factoring.
x2 - 6x + 5 = 0
{1, 5}
What must be true to use the square root method?
b = 0 (No bx term)
If a quadratic equation is in standard form, what is the next thing you should do?
Make sure the a-value is 1
Solve the following quadratic equation by using the quadratic formula: x2 + 6x + 5 = 0
x = -1, x = -5
What is the discriminant?
b2-4ac
Solve the following quadratic equation by factoring.
9x2 - 81x = 0
{0, 9}
What do you look for on a graph when solving by graphing?
x-intercepts
To complete the square, what number should be added to both sides of the equation below?
x2 - 12x = 8
36
Solve the following quadratic equation by using the quadratic formula. Round your answer to the nearest hundredth: x2 - 9x + 6 = 0
{0.72, 8.27}
Name three topics on this week's test.
Solving quadratics by completing the square, solving quadratics by graphing, factoring quadratics, solving quadratics using the quadratic formula, quadratic word problems, solving quadratics using the square root method
Solve the following quadratic equation by using the square root method.
28b2 - 348 =-5
{-7/2, 7/2}
What would you type in Desmos to solve this equation by graphing?
5x2 + 4x - 8 =22 + 2x
5x2 + 2x - 30
Solve the following quadratic equation by completing the square. Round your answers to the nearest hundredth: x2 + 10x +5 = 0
{-0.53, -9.47}
Solve the following quadratic equation by using the quadratic formula: 2x2 + 9x + 4 = 0
{-1/2, -4}
What is the standard form of a quadratic equation?
ax2 + bx + c = 0
Solve the following quadratic equation.
9x2 + 10x - 30= 7x
{5/3, -2}
What is the first step in the square root method?
Solve for (isolate the) x2
When using the completing the square method, what should the next line be?
x2 - 8x + 16 = 2 + 16
(x - 4)2 = 18
Solve the following quadratic equation by using the quadratic formula (nearest tenth):
4x2 - 17x =-12
{0.9, 3.4}
You and a friend are hiking in the mountains. You want to climb to a ledge that is 20ft above you. The height of the grappling hook you throw is given by the function h(t)=-16t2 +32t +5. What is the maximum height of the grappling hook? Can you throw it high enough to reach the ledge?
The max height of the grappling hook is 21ft. This is long enough to reach the 20ft ledge.