Tracy D. answered • 10/26/20

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f(x) = x^{2} - 14x + 45

given in the standard form of: Ax^{2} + Bx + C;

where A = 1, B = -14 and C = 45

- (x,y), the x value of the vertex is x = -2a/b, then use that value to put into f(x) to solve for the y coordinate.

x = (-2)(1)/-14 = -2/-14 = 1/7 (1/7, y)

to find the y coordinate, plug in x = 1/7 ≅.14≅

(1/7)^{2} - 14(1/7) + 45

(1/49) - 2 + 45 ≅ 43.02

So the Vertex is (0.14, 43.02)

- to find the y intercept, just plug x = 0 into the equation, so 0
^{2}- 14(0) + 45 = 45, y intercept = 45 - to find the x intercepts, that is where the y = 0 (or f(x) = 0), so you could set f(x)=0 and factor the equation, set each part = 0 and solve for x.
- 0 = (x+9)(x+5)
- x + 9 = 0; x = -9 and x + 5 = 0; x = -5
- so the x intercepts are at x = -9 and x = -5

Does this process help you understand how to get the answers?

(Please note there is more than one way to get these answers, the other popular way is to complete the square and put it in vertex format.)