write the quadratic equation in standard form that has the roots x=3 and -5

Answer 1

(x-3)(x+5) = 0

x-3 = 0 and x+5=0

x=3 and x=-5 when y=0

y = x^2+2x-15

complete the square

= x^2+2x + 1 -15 - 1

= (x+1)^2 -16

f(x) = y = (x+1)^2 -16

y intercept = -15 or the point (0,-15)

x intercepts = 3 and -5 = the two zeroes or roots, or the points (3,0) and (-5,0)

vertex or minimum point of the upward opening parabola is (-1,-16)

note the 2 zeroes are both 4 units horizontally from the vertex x value, 3 to -1 is 4, and -1 to -5 is 4.

the line of symmetry is x=-1. left and right of x=-1 are mirror images