Answer:
To find the standard form of the equation of a quadratic function with roots of 4 and −1 that passes through (1, −9), we can start by using the fact that if a quadratic function has roots at r1 and r2, its standard form is:
y = a(x - r1)(x - r2)
where "a" is a constant that depends on the function, and (x - r1) and (x - r2) are the factors of the quadratic function.
So, in this case, we have:
r1 = 4
r2 = -1
Passes through (1, -9)
To find "a," we can use the fact that the function passes through (1, -9). Substituting x=1 and y=-9 into the standard form, we get:
-9 = a(1 - 4)(1 - (-1))
-9 = a(-3)(2)
-9 = -6a
a = 1.5
So, the equation of the quadratic function in standard form is:
y = 1.5(x - 4)(x - (-1))
y = 1.5(x - 4)(x + 1)
y = 1.5(x^2 - 3x - 4)
y = 1.5x^2 - 4.5x - 6
Therefore, the answer is y = 1.5x^2 - 4.5x - 6. Option A.
Explanation:
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