What is the value of h when the function is converted to vertex form?

note: vertex form is f(x)=a(x−h)2+k .

f(x)=x2+10x+35

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h =

what is the minimum value for h(x)=x2−16x+60?

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y =

what are the x-intercepts of the quadratic function?

f(x)=x2−3x−10

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let f(x)=x2+17x+72 .

what are the zeros of the function?

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and

let f(x)=x2−8x+19 .

what is the minimum value of the function?

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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 

 

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