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Work Shown:
We will use the general vertex form y = a(x-h)^2+k
(h,k) is the vertex, and the 'a' value stretches or compresses the graph vertically
(h,k) = (-2,18) since the highest point is at (-2,18)
Use either root -8 or 4 to plug into the equation as well. I'll use -8
The root -8 means the point (-8,0) is an x intercept.
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Plug the values mentioned into the equation below. Then solve for 'a'.
y = a(x-h)^2+k
y = a(x-(-2))^2+18 ... plug in (h,k) = (-2,18)
y = a(x+2)^2+18
0 = a(-8+2)^2+18 ... plug in (x,y) = (-8,0)
0 = a(-6)^2+18
0 = a*36+18
0 = 36a+18
36a+18 = 0
36a = -18 ... subtract 18 from both sides
a = -18/36 .... divide both sides by 36
a = (-1*18)/(2*18)
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Alternatively, you could use (x,y) = (4,0), instead of (x,y) = (-8,0), and you'll get the same 'a' value as well.
The value of the leading coefficient of the quadratic function will be negative 1/2. Then the correct option is C.
The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The graph of a quadratic function f has zeros of negative 8 and 4.
Then the factor of the function f(x) will be (x + 8) and (x – 4).
Then the function is given as,
f(x) = a(x + 8)(x – 4)
The function is maximum at (–2,18). Then the leading coefficient of the function will be
18 = a(–2 + 8)(–2 – 4)
18 = a(6)(–6)
a = –18 / 36
a = –1/2
Thus, the value of the leading coefficient of the quadratic function will be negative 1/2.
Then the correct option is C.
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
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