Question

I am extremely confused, can anyone help?​

Answer 1

So I did most of you table for you:

First blank:4

Second blank:-4

Third blank:-8

Fourth blank: Left to you: Just plug in 6 into 1/2x^2-5x+4 (I will check)

Fifth blank: Left to you: Just plug in 8 into 1/2x^2-5x+4 (I will check)

The graph is D.

Explanation:

So they have a table to fill in and they tell you in the first row what they want you to plug in

So the table is asking us to answer this:

What is h(0),h(2),h(4),h(6), and h(8).

h(0) means to replace x with 0 in
`(1)/(2) x^2-5x+4`.

`(1)/(2)(0)^2-5(0)+4`

`0-0+4`

`0+4`

`4`

So the first blank is 4 since h(0)=4.

h(2) means to replace x with 2 in
`(1)/(2) x^2-5x+4`.

`(1)/(2) (2)^2-5(2)+4`

`(1)/(2) (4)-10+4`

`2-10+4`

`-8+4`

`-4`

So the second blank is -4 since h(2)=-4.

h(4) means to replace x with 4 in
`(1)/(2) x^2-5x+4`.

`(1)/(2)(4)^2-5(4)+4`

`(1)/(2)(16)-20+4`

`8-20+4`

`-12+4`

`-8`

So the third blank is -8 since h(4)=-8

Maybe you can try the last 2 blanks in the table part. That is try computing h(6) and h(8). I will check it for you.

Now the points I have so far are (0,4) from the h(0)=4, (2,-4) from the h(2)=-4, and (4,-8) from the h(4)=-8.

I'm looking for a graph that goes through these points (0,4) , (2,-4) , and (4,-8).

By the way the only graphs that are worth looking at is C and D because they are open up. I know my curve for h(x)=1/2x^2-5x+4 should be a parabola open up because 1/2 is positive and 1/2 is the coefficient of x^2.

So Graph C has y-intercept (0,10) not (0,4) so Graph C is not right.

Graph D has y-intercept (0,4). It also goes through (2,-4) and (4,-8).

I don't know if you notice but the x-axis and y-axis are going up by two's in each graph.