write the equation of the parabola that has its vertex at (2, 7) and passes through the point (-1, 3)

Answer 1

Using the vertex form of a parabola, the equation is:

y = a(x - 2)^2 + 7

where "a" is a constant that determines the shape of the parabola.

To find "a," we can use the point (-1, 3) on the parabola:

3 = a(-1 - 2)^2 + 7
3 = a(-3)^2 + 7
3 = 9a + 7
-4 = 9a
a = -4/9

So the equation of the parabola is:

y = (-4/9)(x - 2)^2 + 7

Answer 2

write the equation of the parabola that has its vertex at (5, 0) and passes through the point (7, -2)

Answer 3

Using the vertex form of a parabola, the equation is:

y = a(x - 5)^2 + 0

where "a" is a constant that determines the shape of the parabola.

To find "a," we can use the point (7, -2) on the parabola:

-2 = a(7 - 5)^2 + 0
-2 = 4a
a = -1/2

So the equation of the parabola is:

y = (-1/2)(x - 5)^2 + 0

or

y = (-1/2)x^2 + 5x - 12.5