Question

Which graph correctly solves the system of equations below?

Answer 1

Hello,

answer A is True, others are false

Answer 2

Answer:

one quadratic graph opening down and one quadratic graph opening up. They intersect at 1, negative 1 and negative 1, negative 1

i.e. they intersect at (1,-1) and (-1,-1)

Step-by-step explanation:

We are asked to find which graph correctly solves the system of quadratic equations:

$y=2x^2-3$

and $y=-x^2$

on solving the equation by the method of substitution i.e. on equating both the equations we get:

$2x^2-3=-x^2\\\\2x^2+x^2=3\\\\3x^2=3\\\\x^2=1\\\\x=+1,x=-1$

Now on putting the value of x in any of the equations we get the value of y as:

$y=-1$

Hence, the point of intersections of both the graph is:

(1,-1) and (-1,1).

Also the graph of the quadratic equation:

$y=2x^2-3$

opens upward.

and graph of the quadratic equation:

$y=-x^2$

opens downward.