Graphs and Quadratics
Does the equation below open up or down?
y=-4x^2+3x-11
Down
0=x^2-4
x=+-2
9x^2-64=0
x==+-8/3
Listed below is the quadratic formula for assistance. Give the formula for the discriminant.
(-b+-sqrt(b^2-4ac))/(2a)
b^2-4ac
The following key words tell us we are looking for which peices of the quadratic?
a) "when- highest point"
b) "height- highest point"
c) "ground"
a) x in vertex
b) y in vertex
c) solution (x-intercept)
The axis of symmetry for the equation below.
y=x^2+4x+3
x=-2
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
2x^2+8x+6=0
x=-3,-1
If the discriminant is negative, then there are this many solutions.
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.
The vertex for the equation below.
y=3x^2-6x
(1, -3)
Solve the quadratic.
0=x^2+3x-4
x=-4, 1
11x^2-8x+12=0
No real solution
How many solutions does this equation have?
x^2-8x+16=0
1
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
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.
Solve the quadratic.
x^2+23x-50=0
x=-25,2
x^2-4x=-1
x=2+sqrt3, 2-sqrt3
How many solutions does this equation have?
3/4x^2-6x+17/12
2
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