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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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Respuesta :

samarablue12
answer for q1- (a) f(x)=x^2-6x
x^2-6x+9 = y+9
(x-3)^2 = y+9
Vertex: (3,-9)
ill try to figure out the rest till then:)

Answer:

-5; (8, -4); x = 5 or x = -2; x = -8 or x = -9; (4, 3)

Step-by-step explanation:

For the first question,

To write the function in vertex form, we first set it equal to 0:

0 = x²+10x+35

We want to complete the square.  Our next step will be to take half of b, which is 10, and square it; add this to each side:

(10/2)² = 5² = 25;

0+25 = x²+10x+35+25

25 = x²+10x+25+35

After rearranging the terms, we write the first three as a square.  It will be (x+b/2)²:

25 = (x+5)²+35

Subtract 25 from each side:

25-25 = (x+5)²+35-25

0 = (x+5)²+10

f(x) = (x+5)²+10

This is vertex form.  The value of h will be -5.

For the second question,

To find the minimum we find the vertex.  We first find the axis of symmetry, using

x = -b/2a

x = --16/2(1) = 16/2 = 8

Next substitute 8 in place of x:

f(8) = 8²-16(8)+60 = 64-128+60 = -64+60 = -4

This makes the vertex, or minimum, (8, -4).

For the third question,

We find the roots by writing the function in factored form.  To do this, find factors of c that sum to b:

Factors of -10:  -10 and 1 (sum is -9); 10 and -1 (sum is 9); -5 and 2 (sum is -3); 5 and -2 (sum is 3).  The ones we want are -5 and 2; this gives us

f(x) = (x-5)(x+2)

Using the zero product property,

x - 5 = 0 or x + 2 = 0

x-5+5 = 0+5 or x+2-2 = 0-2

x = 5 or x = -2

For the fourth question,

We want to find the roots again, by writing in factored form:

Factors of 72:  1 and 72 (sum to 73); 2 and 36 (sum to 38); 3 and 24 (sum of 27); 4 and 18 (sum of 22); 6 and 12 (sum of 18); 8 and 9 (sum of 17)

The ones we want are 8 and 9:

f(x) = (x+8)(x+9)

Using the zero product property,

x+8 = 0 or x+9 = 0

x+8-8 = 0-8 or x+9-9 = 0-9

x = -8 or x = -9

For the fifth question, we find the minimum by finding the vertex.  First find the axis of symmetry:

x = -b/2a = --8/2(1) = 8/2 = 4

Substitute 4 in for x:

f(4) = 4²-8(4)+19 = 16-32+19 = -16+19 = 3

The vertex is (4, 3).

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