SOLUTION: How do I grapgh the function that has the following properties: concave up, y-intercept is -6, zeros at x = -2 and x = 3?

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Question 57153This question is from textbook functions modeling change
: How do I grapgh the function that has the following properties: concave up, y-intercept is -6, zeros at x = -2 and x = 3? This question is from textbook functions modeling change

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
How do I grapgh the function that has the following properties: concave up, y-intercept is -6, zeros at x = -2 and x = 3?
This sounds a lot like a U shaped parabola which are formed by quadratic equations.
It's zeros are -2 and 3, so it can be said that:
x=-2
x+2=-2+2
x+2=0
and
x=3
x-3=3-3
x-3=0
A quadratic equation can be made of f(x)=(x+2)(x-3) that makes the parabola go through the x axis at -2 and 3. If we foil the parenthesis we get:
f(x)=x(x-3)+2(x-3)
f(x)=x^2-3x+2x-6
f(x)=x^2-x-6
Notice that if x=0, you'll have a y-intercept of -6.
Also, x^2 is positive so our parabola opens up.
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2-x-6%29
Notice this graph meets all of your requirements.
Happy Calculating!!!