Question

Please help or I’ll fail this :( I need help with C

Answer 1

a. 29

b. g(p) = 2p² -3

c. 4x +2h

Explanation:

You want to evaluate g(x) = 2x²-3 for different values of x.

a. x = -4

Substituting -4 for x, we have ...

`g(-4)=2(-4)^2-3 =2(16)-3\\\\\boxed{g(-4)=29}`

b. x = p

Substituting p for x, we have ...

`\boxed{g(p)=2p^2-3}`

c. Difference quotient

The given expression simplifies to ...

`(g(x+h)-g(x))/(h)=((2(x+h)^2-3)-(2x^2-3))/(h)\\\\=(2(x^2+2hx+h^2))-3-2x^2+3)/(h)=(2x^2+4hx+2h^2-3-2x^2+3)/(h)\\\\=\boxed{4x+2h}`

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Additional comment

The square of a real number is always positive. That should be your first clue that (-4)² = 16 ≠ -16.

Sometimes it helps to remember that an exponent signifies repeated multiplication:

(-4)² = (-4)(-4) . . . . . . has an even number of minus signs, so is positive.

Please note that this is different from -4² = -(4²) = -16.