SOLUTION: Write the linear function for which f (0) = -4 and f (2) = 8. Thank you

Question 146451: Write the linear function for which f (0) = -4 and f (2) = 8.
Thank you
Found 2 solutions by 24HoursTutor.com, jim_thompson5910:
Answer by 24HoursTutor.com(40) (Show Source): You can put this solution on YOUR website!
f(0) = -4
f(2) = 8
Which means f(x) = 3x^2 - 4
Let us check for the given functions :
f(0) = 3X0^2 - 4
= 3X0 - 4
= 0 - 4
= -4
f(2) = 3 X 2^2 - 4
= 3 X 4 - 4
= 12 - 4
= 8
Hence, our ans is f(x) = 3x^2 - 4
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Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm afraid that the previous solution is completely off. The equation "3x^2 - 4" is NOT linear.

f (0) = -4 tells us that when x=0, then y=-4. So the line goes through the point (0,-4)

f (2) = 8 tells us that when x=2, then y=8. So the line goes through the point (2,8)

So let's find the equation of the line that goes through the points (0,-4) and (2,8)

First let's find the slope through the points and

Start with the slope formula.

Plug in , , , , ,

Subtract from to get

Subtract from to get

Reduce

So the slope of the line that goes through the points and is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Rewrite as

Distribute

Multiply

Subtract 4 from both sides.

Combine like terms.

Simplify

So the equation that goes through the points and is

Notice how the graph of goes through the points and . So this visually verifies our answer.
Graph of through the points and

Note: as further confirmation, the graph is a straight line. So this tells us that the equation is linear.
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