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Question 150024: I want to learn this (been 15+ yrs) so I am looking for the why or how answer. I already have the solution(solution manual).
use the vertex abd intercepts to sketch the graph of each quadratic function. give equation of the parabola'a axis of symmetry. use the graph to determine the functions domain and ranges.
f(x)=x^2+3x-10
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! 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)
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