Hi Brandi;
Find an equation of the line containing the pair of points (4, 7) and (0, 4)
Our first priority is to establish slope.
Slope is changeofy divided by changeofx...
m=(yy_{1})/(xx_{1})
m=(74)/(40)
m=11/4
A negative number divided by a negative number has a positive result...
m=11/4
The equation in slopeintercept form is...
y=mx+b
m is the slope.
b is the yintercept, the value of y when x=0.
The slope is (11/4).
In this circumstance, the yintercept is provided as (0,4).
y=(11/4)x+4
Let's use the other equation to verify our results...
7=(11/4)(4)+4
7=11+4
7=7
Determine the vertex of the parabola:
y= 4x^280x+406
The vertex is the value of x at the point of the parabola in which the change of slope is zero. Henceforth, we will take the first derivative of the equation and set this equal to zero...
0=8x80
80=8x
10=x
Let's establish the value of y...
y=4x^{2}80x+406
y=[(4)(10^{2})][(80)(10)]+406
y=[(4)(100)][(80)(10)]+406
y=400800+406
y=400+406
y=6
The vertex is (10,6).
The x value of the vertex can also be established by applying the equation b/2a to the original formula.
y= 4x^280x+406
b/2a
x=[80/(2)(4)]
x=80/8
x=10
Feb 10

Vivian L.