Your answer will be B. -24.
Answer:
Step-by-step explanation:
we know that
A quadratic function in factored form is equal to
where
a is the leading coefficient
x_1 and x_2 are the zeroes of the function
substitute the given values
Find the value of a
Remember that
For x=0 ----> f(0)=4
substitute
so
If the parabola has y = -4 at both x = 2 and x = 3, then since a parabola is symmetric, its axis of symmetry must be between x = 2 and x = 3, or at x = 5/2. Our general equation can then be:
y = a(x - 5/2)^2 + k
Substitute (1, -2): -2 = a(-3/2)^2 + k
-2 = 9a/4 + k
Substitute (2, -4): -4 = a(-1/2)^2 + k
-4 = a/4 + k
Subtracting: 2 = 2a, so a = 1. Substituting back gives k = -17/4.
So the equation is y = (x - 5/2)^2 - 17/4
Expanding: y = x^2 - 5x + 25/4 - 17/4
y = x^2 - 5x + 2 (This is the standard form.)
