Question

How do I graph the parabola? y= -x²

Answer 1

To graph the parabola we can give any numbers for x and then solve for y, or we can find the vertex and then go to either way.

0. Finding the vertex.

The x value of the vertex's coordinate can be calculated as follows:

`x=(-b)/(2a)`

where a and b represent the coefficients of the equation of the parabola in the form:

`ax^2+bx+c=0`

As our parabola is:

`y=-x^2`

we can see that a = -1 and b = 0. Replacing this in the formula for the x coordinate:

`x=(0)/(2(-1))=0`

We have to replace this value in the equation:

`y=-(0)^2=0`

Then the vertex can be found in (0,0).

Now we have to find different coordinates in each side to graph the parabola by giving arbitrarily numbers to x and evaluating them in the equation.

• x = 1

`y=-(1)^2=-1`

Then the coordinate, in this case, is (1, -1)

• x = -2

`y=-(-2)^2=-(4)=-4`

The coordinate, in this case, is (-2, -4).

• x = 3

`y=-(3)^2=-9`

The coordinate is (3, -9).

• x = -4

`y=-(-4)^2=-(16)=-16`

The coordinate is (-4, -16).

We can keep choosing any value for x to find y and get the coordinate in need be.

Answer:

• (0,0)

,

• (1, -1)

,

• (-2, -4)

,

• (3, -9)

,

• (-4,-16)