Question

Which graph correctly solves the system of equations below?

y = − x2 + 1
y = x2 − 4

Answer 1

A)

Answer 2

Is that x to the power 2, or 2 times x?

Answer 3

\[y = x^2 + 1\]

Answer 4

Right, got it.

Answer 5

B)

Answer 6

C)

Answer 7

D)

Answer 8

It's definitely C. When you have a quadratic equation of the form ax^2 + bx + c = 0 where a, b and c are constants then a will be the degree to which the graph is stretched and if it is negative it will reflect the graph along the x-axis, b will shift the graph to the right if its sign is negative and vice versa and c is the y-intercept.

Answer 9

Thankyou so much!

Answer 10

This means the graph y = -x^2 + 1

Is an upside down parabola from the - sign

Is not stretched (though this is not very relevant except in comparison) from the fact that a = 1

Cuts the y-axis at y = 1

Now both B and C have these basic features but looking at y = x^2 - 4 we see that this graph is an unstretched, right way up parabola with an intercept at y = -4

But B has a somewhat squashed (another way of stretching) while c isn't thus, it is c