On the curve included:

f(x)= 10 - 3x - x2 (x squared) 

how do I find points a, b and c?


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Expert Answers

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We are given the graph of the function `f(x)=-x^2-3x+10 ` and we are asked to find the points a,b, and c as indicated on the graph.

Note that a and b are the x-intercepts, while c is the y-intercept.

(1) c is the easiest to find: the y-intercept occurs when x=0. Then f(0)=10, so the point c is at (0,10).

(2) The x-intercepts can be found in a few different ways. Since the quadratic function has x-intercepts, then the roots or zeroes of the function are real (and the same as the x-intercepts.) So we can factor the function (if possible) or use completing the square or the quadratic formula to find the roots.

`-(x^2+3x-10)=0 `

`-(x+5)(x-2)=0 ==> x=-5, x=2 `


Thus a=(-5,0), b=(2,0), and c=(0,10)


The graph:

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