Answer:
a. 4, 6
b. -72
c. (5, 3)
d. Graph A
Step-by-step explanation:
a.
To answer these questions, it is useful to start by factoring the equation.
y = -3x² +30x -72 . . . . given
y = -3(x² -10x +24) . . . . factor out leading coefficient
y = -3(x -4)(x -6)
The x-intercepts are the values of x that make the factors zero:
x = 4, 6
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b.
The y-intercept is the constant in the equation: -72.
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c.
We know the x-coordinate of the vertex is the midpoint between the x-intercepts: (4+6)/2 = 5. The y-coordinate can be found by evaluating y at that x-value.
y = -3(5 -4)(5 -6) = -3(1)(-1) = 3
The vertex is (5, 3).
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d.
The graph that has the correct vertex and x-intercepts is Graph A.
