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 Enter your answer in the box. h = What is the minimum value for h(x)=x2−16x+60? Enter your answer in the box. y = What are the x-intercepts of the quadratic function? f(x)=x2−3x−10 Enter your answers in the boxes. Let ​ f(x)=x2+17x+72 ​ . What are the zeros of the function? ​Enter your answers in the boxes. ​ and Let ​ f(x)=x2−8x+19 ​ . What is the minimum value of the function?​ Enter your answer in the box. ​

Question
Answer:
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 squaresf(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 equationh(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=-8x=-9Part 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 squaresf(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 
 
solved
general 6 months ago 2551