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:
[tex]x=\frac{-b}{2a}[/tex]where a and b represent the coefficients of the equation of the parabola in the form:
[tex]ax^2+bx+c=0[/tex]As our parabola is:
[tex]y=-x^2[/tex]we can see that a = -1 and b = 0. Replacing this in the formula for the x coordinate:
[tex]x=\frac{0}{2(-1)}=0[/tex]We have to replace this value in the equation:
[tex]y=-(0)^2=0[/tex]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
[tex]y=-(1)^2=-1[/tex]Then the coordinate, in this case, is (1, -1)
• x = -2
[tex]y=-(-2)^2=-(4)=-4[/tex]The coordinate, in this case, is (-2, -4).
• x = 3
[tex]y=-(3)^2=-9[/tex]The coordinate is (3, -9).
• x = -4
[tex]y=-(-4)^2=-(16)=-16[/tex]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)
