Question

Miss gatlin tosses a donut in the air to one of her students. The path of the donut makes a parabolic curve. She already knows that the equation will be set up the following way:y =a (x_15)^2+18 and goes through the point (2,7).

Answer 1

The value of 'a' in the parabolic equation y = a(x - 15)^2 + 18, when the parabola goes through the point (2, 7), is calculated by substitution and determined to be -11/169.

Step-by-step explanation:

The question involves finding the value of 'a' in the quadratic equation of a parabola representing the trajectory of a tossed donut: y = a(x - 15)^2 + 18, given that the parabola goes through the point (2, 7). To solve for 'a', we substitute the given point into the equation.

Substituting x = 2 and y = 7, we get:

7 = a(2 - 15)^2 + 18

Now, let's proceed with the calculation:

7 = a(-13)^2 + 18

7 = 169a + 18

Subtracting 18 from both sides:

-11 = 169a

Dividing by 169 to solve for 'a':

a = -11/169

Therefore, the constant 'a' in the equation of the parabola is -11/169.