a) Find the equation of the line that passes through the given points. (Use x as

sibuzwaW

sibuzwaW

Answered question

2021-11-06

a) Find the equation of the line that passes through the given points. (Use x as your variable.)
(0, 7), (8, 0)
y=?
b) Find the vertex of the graph of the equation.
y=x29
(x, y)=()
c) Find the minimum or maximum value of the quadratic function.
f(x)=x28x+8
()?
d) Find the minimum or maximum value of the quadratic function.
f(x)=2x2+8x5
()?

Answer & Explanation

Demi-Leigh Barrera

Demi-Leigh Barrera

Skilled2021-11-07Added 97 answers

Step 1
Straight Line:
The given points are (0, 7), (8, 0)
The slope of the points is (m)=y2y1x2x1
Here (x1, y1)=(0, 7) & (x2, y2)=(8, 0)
m=78
Therefore the equation be
y=mx+c
y=78x+c
it is pas sin g through the point (0, 7)
7=c
y=78x+7
8y+7x=7
Step 2
y=x29
We need to find vertex of the parabola.
y+9=x2
The vertex of the parabola is (0, -9).
Step 3
f(x)=x28x+8
For maximum and minimum value we need to find f(x) and then put f(x)=0
Now we should check for which value f(x)>0 or <0.
f(x)=2x8
f(x)=0
2x8=0
x=4
f(x)=2>0 (so there is only minimum value possible)
f(4)=428×4+8
=8
This is the required minimum value.
Step 4
f(x)=2x2+8x5
For maximum and minimum value we need to find f(x) and then put f(x)=0
Now we should check for which value f(x)>0 or <0.
f(x)=4x+8
f(x)=0
4x+8=0
x=2
f(x)=4<0 (so there is only maximum value possible)
f(2)=2×(2)2+8×25
=3
This is the required maximum value.
This is the required minimum value.

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