Question

Graph the parabola.y=x2-4Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-functionbuttonХ5?

Answer 1

Given the Quadratic Function:

$y=x^2-4$

You need to remember that the Quadratic Parent Function (the simplest form of a Quadratic Functions) is:

$y=x^2$

And its vertex is at the Origin:

$(0,0)$

The function given in the exercise was obtained by shifting the parent function 4 units down. That means that the y-coordinate of the vertex changes, but the x-coordinate is the same. Therefore, the vertex of this parabola is:

$(0,-4)$

To find two points to the left of the vertex, you can choose this value for "x":

$x=-1$

Substituting this value into the function and evaluating, you can find the corresponding value of "y":

$y=(-1)^2-4=1-4=-3$

Now you have this point:

$(-1,-3)$

You can choose this value of "x":

$x=-4$

And apply the same procedure:

$y=(-4)^2-4=16-4=12$

Then, the other point is:

$(-4,12)$

To find the first point to the right of the vertex, you can substitute this value of "x" into the function and evaluate:

$x=1$

Then, you get:

$y=(1)^2-4=-3$

The point is:

$(1,-3)$

To find the second point, substitute this value into the equation and evaluate:

$x=4$

Then:

$y=(4)^2-4=16-4=12$

So the other point is:

$(4,12)$

Now you can plot the points and graph the function.

Therefore, the answer is: