Factoring
Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0
x = 7 x = -2
Dianne dove from the 10-m diving board. Her height h, in meters, above the water when she is x meters away from the end of the board is given by
h = -(x - 1)2 + 11.
What her maximum height?
11 metres
Simplify sqrt12
+ 2 sqrt 3 and - 2 sqrt 3
What is the quadratic formula?
x = -b +- sqrt(b^2 - 4ac) all over 2a
Find the vertex of y=-x^2+8x-15
(4,1)
Solve the following quadratic equation by factoring. x2+ 3x + 2 = 0
x = -2 x = -1
Van dives off a 4-m springboard. His height, h, in meters, above the surface of the water is defined by the relation h = -d2 + 3d + 4. Where will he enter the water?
at 4 meters
Simplify 2+- sqrt 96 all over 2
1+- 2sqrt6
Solve the following quadratic equation by using the quadratic formula: x^2 + 6x + 5 = 0
x = -1 x = -5
Find the vertex of y=x^2-2x
(1,-1)
Solve the following quadratic equation by factoring. x2 - 6x + 5 = 0
x = 5 x = 1
A square was altered so that one side is increased by 9 inches and the other side is decreased by 2 inches. The area of the resulting rectangle is 60 inches squared. What was the area of the original square??
36 inches squared
Multiply (4x+3)(5x-2)
20x2+7x-6
Solve the following quadratic equation by using the quadratic formula: x^2 - 9x + 20 = 0
x = 5 x = 4
Find the vertex of y=5x^2+2x-2
(-1/5,-11/5)
Solve the following quadratic equation by factoring. x2 - 6x - 27 = 0
x = 9 x = -3
A circus acrobat is shot out of a cannon with an initial speed of 50 ft/s. The equation for the acrobat's pathway can be modeled by the equation h=-16t2+50t+4. Find the maximum height of the acrobat. And how long will it take to reach the ground??
43.06 ft and 3.2 seconds
y=-x2-4x+1, what is its vertex?
(-2,5)
Solve the following quadratic equation by using the quadratic formula: 2x^2 + 9x + 4 = 0
x = -1/2 x = -4
Change from Vertex Form to Standard Form
y=-5(x-1)2+4
-5x2+10x-1
Solve the following quadratic equation by factoring. 2x2 - 5x - 3 = 0
x = -1/2 x = 3
A soccer ball is kicked from the ground. The soccer ball reaches a maximum height of 2.5 meters and travels a horizontal distance of 1 meter. In the context of the given situation, what do the intercepts and maximum point represent? - include what they are
(0,0) - y-intercept/x-intercept, starting height of the ball is 0 meters
(0.5,2.5) - max/vertex, the ball reaches 2.5 meters high and a horizontal distance of 0.5 meters
(1,0) - y-intercept/x-intercept, the ball landing 1 meter from the starting point
The parent function f(x)=x2 is vertically stretched by a factor of 5 and translated 12 right and 8 units up. What is the quadratic function in vertex form?
g(x)=5(x-12)2+8
Solve the following quadratic equation by using the quadratic formula: 4x^2 - 17x - 15 = 0
x = 5 x = -3/4
Vertex: (2,5)
Point: (3,7)
What is the equation for this parabola in vertex form
y=2(x-2)2+5