Answer:
- x-intercepts: -1, 5
- vertex: (2, -9)
Explanation:
The factors of -5 that add to give -4 are -5 and +1. So, the equation can be factored as ...
y = (x -5)(x +1)
The x-intercepts are the values of x that make these factors be zero.
x = 5 makes the first factor 0
x = -1 makes the second factor 0
The x-intercepts are x = -1, 5.
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The x-coordinate of the vertex is halfway between the x-intercepts, so can be found by averaging their values.
vertex x-coordinate = (-1 +5)/2 = 2
The y-coordinate of the vertex is the value of y for that value of x:
y = (2 -5)(2 +1) = (-3)(3) = -9 . . . . . filling x=2 into the factored equation
The vertex is (x, y) = (2, -9).
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A graphing calculator can confirm these values for you.