Part 1) What is the value of h when the function is converted to vertex form?
f(x)=x²+10x+35
Group
terms that contain the same variable
f(x)=(x²+10x)+35
Complete
the square . Remember to balance the equation
f(x)=(x²+10x+25)+35-25
Rewrite as perfect squares
f(x)=(x+5)²+10
(h,k) is (-5,10)
the answer Part 1) is
h is -5
Part 2) What is the minimum value for h(x)=x²−16x+60?
h(x)=x²−16x+60
Group terms that contain the same variable
h(x)=(x²−16x)+60
Complete the square . Remember to balance the equation
h(x)=(x²−16x+64)+60 -64
Rewrite as perfect squares
h(x)=(x-8)²-4
(h,k) is the vertex> (8,-4)
the answer Part 2) is
the minimum value of h(x) is -4
Part 3)
What are the x-intercepts of the quadratic function?
f(x)=x²−3x−10
we know that the x intercepts is when y=0
x²−3x−10=0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(x²−3x)=10
Complete
the square. Remember to balance the equation by adding the same constants
to each side
(x²−3x+2.25)=10+2.25
Rewrite as perfect squares
(x-1.5)²=12.25> (+/-)[x-1.5]=3.5
(+)[x-1.5]=3.5> x1=5
(-)[x-1.5]=3.5> x2=-2
the answer Part 3) is
the x intercepts are
x=5
x=-2
Part 4) Let f(x)=x²+17x+72 .
What are the zeros of the function?
x²+17x+72=0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(x²+17x)=-72
Complete
the square. Remember to balance the equation by adding the same constants
to each side
(x²+17x+72.25)=-72+72.25
Rewrite as perfect squares
(x+8.5)²=0.25> (+/-)[x+8.5]=0.5
(+)[x+8.5]=0.5> x1=-8
(-)[x+8.5]=0.5> x2=-9
the answer part 4) is
x=-8
x=-9
Part 5) Let f(x)=x2−8x+19 .
What is the minimum value of the function?
f(x)=x²−8x+19
Group
terms that contain the same variable
f(x)=(x²−8x)+19
Complete
the square. Remember to balance the equation
f(x)=(x²−8x+16)+19-16
Rewrite as perfect squares
f(x)=(x-4)²+3
the vertex is the point (4,3)
the answer Part 5) is
the minimum value of the function is 3
16
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