Question 150024
15 years, huh...congratulations


for an expression of the form ax^2+bx+c, the equation for the axis of symmetry is x=-b/(2a)


since the vertex lies on the axis of symmetry,
__ substituting this x value into the equation of the function will give the y value (and thus the coordinates) of the vertex


the intercepts, where the graph crosses an axis, are found by substituting zero for x or y and solving for the other
__ this is because when you are crossing an axis, the value of the other component is zero


axis of symmetry __ x=-3/(2*1) __ x=-3/2


vertex __ y=(-3/2)^2+3(-3/2)-10 __ y=9/4-9/2-10 __ y=-49/4
__ so (-3/2,-49/4) is the location of the vertex


intercepts __ substituting 0 for x __ y=0^2+3(0)-10 __ y=-10 __ this is the y intercept


substituting 0 for y __ 0=x^2+3x-10 __ factoring __ 0=(x+5)(x-2)
x+5=0 __ x=-5
x-2=0 __ x=2
these are the x intercepts (the axis of symmetry is midway between them)