Question

Solve the system of equations below by graphing. x^2-2x+y-3=0 x2+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

Answer:

$(-1.5,-2.25)$

Step-by-step explanation:

The first function is $x^2-2x+y-3=0$.

We make y the subject of this function to obtain,

$y=3+2x-x^2$.

This is graph will open downwards because $a=-1\:$.

At  y-intercept of this graph, $x=0$.

$\Rightarrow y=3+2(0)-(0)^2$

$\Rightarrow y=3$

The y-intercept is $(0,3)$.

At x-intercept $y=0$.

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

$0=(x+1)(x-3)$

$\Rightarrow x=-1,x=3$.

The x-intercepts are,

$(-1,0),(3,0)$

Also the vertex form of the function is,

$y=-(x-1)^2+4$.

Therefore the vertex of the parabola is $(1,4)$.

We plot all the points obtained and draw a smooth curve to obtain the curve as show in the diagram.

The second function is

$x^2+y=0$

$\Rightarrow y=-x^2$

This is the graph of the basic quadratic function $y=x^2$ that has been turned upside down.

This graph also has the vertex,y-intercept and x-intercept all at $(0,0)$.

We now graph this too on the same graph sheet as the first one to obtain the blue graph as shown in the diagram.

These two graphs intersect at the point, $(-1.5,-2.25)$.

Therefore the correct answer is B