Find intercept form for points (1,0) and (5,0) and vertex (3,3).
3 = a(3-1)(3-5)
3 = a(2)(-2)
3 = -4a
a = -3/4
intercept form is: 3 = -3/4(3-1)(3-5)
Find intercept form with points (2,0) and (8,0) with vertex (5,3).
3 = a(5-2)(5-8)
3 = a(3)(-3)
3 = -9a
a = -1/3
Therefore, intercept form for points (2,0) and (8,0) with vertex (5,3) is 3 = -1/3(5-2)(5-8)
Despite my stresses and self conclusion during the linear equation section I was able to complete this challenge with objective ease without peeking. I still intend to plod on through regardless but this has cheered me up a little.
Edit - just realised I forgot the negatives on the fractions in the final answers, dammit, so close.
Can I ask if this is really necessary to take into account? Since when you put the values of p and q into the formula “y = a(x - p)(x - q)” you are actually sayng “y = a(x + (-1(p))) (x + (-1(q)))” so even if the value is negative or positive, the formula will inverse it’s value at the end so it can adds to x in order to turn it into 0?
So, if I have the values (-12, 0) and (25, 0) for the roots, the formula will be: y = a(x + (-1(-12))) (x - (-1(25))) which will turn into y = a(x + 12) (x - 25).
For the first part, the higher projectile with vertex (3,3), I got:
0 = -(3/4)(x - 1)(x - 5)
On the next challenge, with volcanoes farther apart with roots at (2,0) and (8,0), vertex at (5,3), I got:
0 = -(1/3)(x - 2)(x - 8)
