If we transform y = x2 by 5 units to the left and 8 units up, what is the vertex of the resulting parabola?

Step-by-step explanation:

The given function is

Notice that this is a parent function, that is, the simplest form of a quadratic function.

The transformations are:

Notice that this are rigid transformations, specifically, they are translations only.

Remeber, to move a function to the left, we must sum units to the x-variable. To move a function upwards, we must sum units to the y-variable.

Therefore, the transformed function is

Notice that the equation has the form .

Where , and .

Additionally, an important property of quadratic function is the vertex of the parabola which represents the function, which is at

Therefore, in this case, the vertex is at

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

what is the original number? you forgot to add it.