To find the equation of the parabola that passes through the points (-1,0), (4,0), and (5,-18), we can use the form y=a(x–p)(x–q), where p and q are the x-intercepts of the parabola.

From the points given, we can see that the parabola intercepts the x-axis at x=-1 and x=4. So, p=-1 and q=4.

Now, we have y=a(x+1)(x-4).

To find the value of 'a', we can use the third point (5,-18). Substitute x=5 and y=-18 into the equation:

-18=a(5+1)(5-4)
-18=a(6)(1)
-18=6a
a=-18/6
a=-3

So, the equation of the parabola is y=-3(x+1)(x-4).

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To find the equation of the parabola that passes through the points (-1,0), (4,0), and (5,-18), we can use the form y=a(x–p)(x–q), where p and q are the x-intercepts of the parabola.

From the points given, we can see that the parabola intercepts the x-axis at x=-1 and x=4. So, p=-1 and q=4.

Now, we have y=a(x+1)(x-4).

To find the value of 'a', we can use the third point (5,-18). Substitute x=5 and y=-18 into the equation:

-18=a(5+1)(5-4)
-18=a(6)(1)
-18=6a
a=-18/6
a=-3

So, the equation of the parabola is y=-3(x+1)(x-4).

Knowee AI · Accepted Answer

To find the equation of the parabola that passes through the points (-1,0), (4,0), and (5,-18), we can use the form y=a(x–p)(x–q), where p and q are the x-intercepts of the parabola.

From the points given, we can see that the parabola intercepts the x-axis at x=-1 and x=4. So, p=-1 and q=4.

Now, we have y=a(x+1)(x-4).

To find the value of 'a', we can use the third point (5,-18). Substitute x=5 and y=-18 into the equation:

-18=a(5+1)(5-4)
-18=a(6)(1)
-18=6a
a=-18/6
a=-3

So, the equation of the parabola is y=-3(x+1)(x-4).

Write the equation of the parabola that passes through the points shown in the table.x y–1 04 05 –18Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.Submit

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