Question

Solve the system of equations below by graphing.

x^2-2x+y-3=0
x^2+y=0

What is the solution rounded to the nearest hundredth?
(–2.25, –1.5)
(–1.5, –2.25)
(–0.82, –0.68)
(–0.68, –0.82)

Answer 1

B.(–1.5, –2.25)

Explanation:

Answer 2

The correct answer is B

EXPLANATION

The first function is

`x^2-2x+y-3=0`

We make y the subject to obtain;

`y=-x^2+2x+3`

Let us quickly write this in the vertex form.

`y=-(x^2-2x)+3`

`y=-(x^2-2x+(-1)^2)+3+(-1)^2`

`y=-(x-1)^2+4`

Since the
`a` is negative, the graph opens up.

The vertex is at
`(1,4)`

The y-intercept is
`-3`

The x-intercept is found by equating the function to zero.

`-(x-1)^2+4=0`

`\Rightarrow (x-1)^2=4`

`\Rightarrow (x-1)=\pm 2`

`\Rightarrow x=1 \pm2`

`\Rightarrow x=-1,3`

With these information we can quickly sketch the graph as shown in the attachment(the red graph).

For the second function,

`x^2+y=0`

we again make y the subject to obtain,

`y=-x^2`

This is a basic quadratic function that can be graphed easily. Note that it is also a maximum graph.

From the graph the solution to the two functions is

`(-1.5,-2.25)`