the y-intercept is found by setting x equal to 0 and solving for y.
start with:
y = 3 * (x-5/2)^2 - 75/4
replace x with 0 to get:
y = 3 * (-5/2)^2 - 75/4
simplify to get:
y = 3 * (25/4) - 75/4
simplify further to get:
y = 75/4 - 75/4
simplify further to get:
y = 0
y = 0 is your y-intercept.
the coordinate point is (0,0).
now you want to find the x-intercepts.
start with:
y = 3 * (x-5/2)^2 - 75/4
set y = 0 and switch the sides of the equation to get:
3 * (x-5/2)^2 - 75/4 = 0
you can switch the sides of the equation because of the property of equations that says "if a = b, then b = a".
add 75/4 to both sides of the equation to get:
3 * (x-5/2)^2 = 75/4
divide both sides of the equation by 3 to get:
(x-5/2)^2 = 75/12
take the square root of both sides of the equation to get:
x-5/2 = plus or minus sqrt(75/12)
add 5/2 to both sides of the equation to get:
x = 5/2 plus or minus sqrt(75/12)
sqrt(75/12) is equal to sqrt((3*25)/(3*4))
the 3 in the numerator and denominator cancel out and you are left with:
sqrt(75/12) is equal to sqrt(25/4)
sqrt(25/4) is equal to sqrt(25) / sqrt(4) which is equal to 5/2.
sqrt(75/12) is therefore equal to 5/2.
your equation of:
x = 5/2 plus or minus sqrt(75/12) becomes:
x = 5/2 plus or minus 5/2
solve for x to get:
x = 0 or x = 5
your solution is complete.
you have:
x-intercepts are x = 0 and x = 5
y-intercept is y = 0
coordinate points of the x-intercepts are (0,0) and (5,0).
coordinate point of the y-intercept is (0,0).
a graph of your equation of y = 3 * (x-5/2)^2 - 75/4 is shown below.
note that 75/4 is equal to 18.25 an that 5/2 is equal to 2.5.
