Answer:
see below
Step-by-step explanation:
f(x) = −16x^2 + 24x + 16
Set equal to zero to find the x intercepts
0 = −16x^2 + 24x + 16
Factor out -8
0 = -8(2x^2 -3x-2)
Factor
0 = -8(2x +1) (x-2)
Using the zero product property
2x+1 =0 x-2 =0
x = -1/2 x=2
The x intercepts are -1/2 ,2
Since the coefficient of x^2 is negative the graph will open down and the vertex will be a maximum
The x value of the maximum is 1/2 way between the zeros
(-1/2+2) /2 = 1.5/2 =.75
To find the y value substitute into the function
f(.75) = -8(2x +1) (x-2)
=-8(2*.75+1) (.75-2)
= -8(2.5)(-1.25)
=25
The vertex is at (.75, 25)
We have the zeros, and the vertex. We know the graph is symmetrical about the vertex
Answer:
Usually it's in standard form: ax²+bx+c
or vertex form: y=a(x-h)²+k
If you put the graph into a graphing calculator it's going to look like a hill/depression.
Step-by-step explanation:
Standard form ex: 3x²+2x+1
Vertex form ex: y=4(x-1)²-2
Don't trust those link my cuz
A. Is not linear because is has no y
How this helped ya out! :D
Answer: 3.675 seconds
Step-by-step explanation:
Hi, when the object hits the ground, h=0:
h=−16t^2+48.6t+37.5
0=−16t^2+48.6t+37.5
We have to apply the quadratic formula:
For: ax2+ bx + c
x =[ -b ± √b²-4ac] /2a
Replacing with the values given:
a=-16 ; b=48.6; c=37.5
x =[ -(48.6) ± √(-48.6)²-4(-16)37.5] /2(-16)
x = [ -48.6 ± √ 4,761.96] /-32
x = [ -48.6 ± 69] /-32
Positive:
x = [ -48.6 + 69] /-32 = -0.6375
Negative:
x = [ -48.6 - 69] /-32 = 3.675 seconds (seconds can't be negative)
Feel free to ask for more if needed or if you did not understand something.