Question

This question has two parts.

Consider the functions f(x)
and g(x),
with equations shown below.

f(x)=3x^2−50x+80

g(x)=−2x^2+13x+100



Part A

Let h(x)=f(x)−g(x)

Write h(x)
as a polynomial function in standard form: h(x)=ax^2+bx+c

Determine the values of a, b,
and c.

(3 points)
a=


b=


c=


Question 2
Part B

Evaluate f(1)−g(1)

(1 point)
f(1)−g(1)=

Answer 1

To solve Part A, let's first find \( h(x) = f(x) - g(x) \) by substituting the expressions for \( f(x) \) and \( g(x) \).

We have:
\[
f(x) = 3x^2 - 50x + 80
\]
\[
g(x) = -2x^2 + 13x + 100
\]

Now, we calculate \( h(x) \):
\[
h(x) = f(x) - g(x) = (3x^2 - 50x + 80) - (-2x^2 + 13x + 100)
\]

Distributing the negative sign:
\[
h(x) = 3x^2 - 50x + 80 + 2x^2 - 13x - 100
\]

Now, combine like terms:
- For \( x^2 \) terms: \( 3x^2 + 2x^2 = 5x^2 \)
- For \( x \) terms: \( -50x - 13x = -63x \)
- For constant terms: \( 80 - 100 = -20 \)

Putting it all together:
\[
h(x) = 5x^2 - 63x - 20
\]

Thus, in standard form \( h(x) = ax^2 + bx + c \), we have:
- \( a = 5 \)
- \( b = -63 \)
- \( c = -20 \)

### Part A Answers:

- \( a = 5 \)
- \( b = -63 \)
- \( c = -20 \)

---

Now, for Part B, we need to evaluate \( f(1) - g(1) \).

First, calculate \( f(1) \):
\[
f(1) = 3(1)^2 - 50(1) + 80 = 3 - 50 + 80 = 33
\]

Now, calculate \( g(1) \):
\[
g(1) = -2(1)^2 + 13(1) + 100 = -2 + 13 + 100 = 111
\]

Finally, subtract \( g(1) \) from \( f(1) \):
\[
f(1) - g(1) = 33 - 111 = -78
\]

### Part B Answer:

\( f(1) - g(1) = -78 \)