Question

Polynomial functions need help on questions 4 6 8 10

Answer 1

4) h(-1/2) = 5/8

8) k(a²) = a⁴ + 3

Step-by-step explanation

4)

h(-1/2) means that we have to replace t by -1/2 into h(t):

`h\mleft(-(1)/(2)\mright)=-2\mleft(-(1)/(2)\mright)-(3)/(2)\cdot\mleft(-(1)/(2)\mright)^2`

Since this has all numbers we can find a numeric answer:

`\begin{gathered} h\mleft(-(1)/(2)\mright)=1-(3)/(2)\cdot(1)/(4) \\ h\mleft(-(1)/(2)\mright)=1-(3)/(8) \\ h\mleft(-(1)/(2)\mright)=(5)/(8) \end{gathered}`

8) This is similar to problem 4, but instead of having numbers we just have to replace by an expression. k(a²) means to replace a by a² in k(a):

`k(a^2)=(a^2)^2+3`

In this case we don't have numbers to solve, but we can simplify this expression by using the property of exponent of exponents:

`\begin{gathered} k(a^2)=a^(2\cdot2)+3 \\ k(a^2)=a^4+3 \end{gathered}`