Question

Please find the points of intersection of the equation below and answers should be in ordered pairs!!

Answer 1

Given:

`y=-x^2+x+3\text{ and y=-}(1)/(2)x+3`

To find the points of intersection, we have:

`-x^2+x_{}+3=-(1)/(2)x+3`

Solve for x:

`\begin{gathered} -x^2+x+(1)/(2)x=3-3 \\ \\ -x^2+(3)/(2)x=0 \\ \\ -x(x-(3)/(2))=0 \\ x\text{ =0 or }1.5 \end{gathered}`

Now input 0 for x in equation 1 and 1.5 for x in equation 2

`\begin{gathered} y=0^2^{}+0+3 \\ y\text{ = 3} \end{gathered}`
`\begin{gathered} y\text{ = -}(1)/(2)(1.5)+3 \\ \text{ y = -}(3)/(4)+3 \\ y\text{ = }(9)/(4)=2.25 \end{gathered}`

Thus, the points of intersection for both lines are:

`(1.5,\text{ 2.25) and }(0,\text{ 3)}`

ANSWER:

(1.5, 2.25) and (0, 3)