Respuesta :
Let h(x) = 0.
Set each factor to 0 and solve for x.
-(x - 5) = 0
Disregard the negative sign in front of the parentheses.
x - 5 = 0
x = 5 is a zero.
x - 13 = 0
x = 13 is another zero.
The smaller zero is 5.
The larger zero is 13.
Both numbers make the quadratic function become zero.
Use the FOIL METHOD to express h(x) in standard form.
h(x) = -(x - 5)*x - 13)
After using FOIL, we get -x^2 + 18x - 65.
The square x term has a -1 in front. This number is the value of a in the formula below. The coefficient of x is 18. This is our b value.
x = -b/2a
x = -(18)/2(-1)
x = 18/2
x = 9
This number 9 just found is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, replace every x you see in the quadratic equation above with 9 and simplify.
h(9) = -(9)^2 + 18(9) - 65
h(9) = 16
The vertex is located at the point (9, 16).
The smaller zero is 5 and larger zero is 13. The vertex is located at the point (9, 16).
How to find the vertex of the parabola?
Let h(x) = 0.
A. Now Set each factor to 0 and solve for x.
-(x - 5) = 0
Disregard the negative sign;
x - 5 = 0
x = 5 is a zero.
x - 13 = 0
x = 13 is another zero.
The smaller zero is 5 and larger zero is 13.
B. Both numbers make the quadratic function become zero.
So, Use the FOIL METHOD to express h(x) in standard form.
h(x) = -(x - 5)(x - 13)
we get -x^2 + 18x - 65.
x = -b/2a
x = -(18)/2(-1)
x = 18/2
x = 9
Hence, This number 9 just found is the x-coordinate of the vertex.
In order to find the y-coordinate of the vertex, replace every x you see in the quadratic equation above with 9 and simplify;
h(9) = -(9)^2 + 18(9) - 65
h(9) = 16
Hence, The vertex is located at the point (9, 16).
Learn more about the vertex form here:
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