Question

Which graph correctly solves the system of equations below?

y = 2x2 − 3
y = −x2

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

one quadratic graph opening up and one quadratic graph opening down. They intersect at 0, negative 3.

two quadratic graphs opening up. They intersect at 0, negative 3.

quadratic graph opening up and quadratic graph opening down. They intersect at 1, 2 and negative 1, 2

Answer 1

Hello,

answer A is True, others are false

Answer 2

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)

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.