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3 years ago

How do I convert standard form into vertex form when there is no perfect square

Mathematics

1 answer:

balu736 [363]3 years ago

5 0

Answer:

To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you have to Get ready to create a perfect square trinomial. BUT be careful!! In previous completing the square problems with a leading coefficient not 1, ... Take half of the coefficient of the x-term inside the parentheses, square it, and place it in the box.

hope this helps :)

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Use the graph of f at the right to complete each of the parts (a) through (h)

Maru [420]

Answers:

a. The domain of f is ]-∞ , ∞[

b. The range of f is [-4 , ∞[

c. f(1) = 5

d. The vales of x for which f(x) is -3 are 7 and 9

e. The points at which the graph crosses the x-axis are (6,0) and (10,0)

f. The point where the graph of f crosses the y-axis is (0,5)

g. The values of x for which f(x) < 0 are ]6 , 10[

h. f(-7) is positive

Explanation:

Part a:

The domain of the function refers to all the possible x-values that can be used as an input for this function.

Taking a look at the graph, we can see that the graph extends endlessly from both ends of the x-axis. This means that all x-values can be used as a domain for the function. In other words, the domain of the function is all the real numbers.

In interval notation, this is written as:

Domain = ]-∞ , ∞[

Part b:

The range of the function refers to all the possible y-values that can be used as an output for the function.

From the graph, we can note that the function extends endlessly in the direction of the positive y-axis while it stops at a value of -4 in the direction of the negative y-axis.

This means that the range of the function starts from -4 (included) and extends to positive infinity.

In interval notation, this is written as:

R = [-4 , ∞[

Part c:

f(1) means that we are looking for the output (the value of y) for which the input (the value of x) is 1.

From the graph, we start by searching for x=1 (first square edge after the origin) and then move vertically till we intersect the graph.

Doing this, we will find that the value of y at x=1 is 5

Therefore:

f(1) = 5

Part d:

f(x) = -3 means that the output value (the value of the y) for the certain input (value of x) is -3

To get the value of x, we go y=-3 and move horizontally till we intersect the graph.

Doing this, we will find that the value of y is -3 at x = 7 and x = 9

Part e:

The points where the graph crosses the x-axis are the points that have y-value equal to 0

Checking the graph, we can note that the function crosses the x-axis at two points which are (6,0) and (10,0)

Part f:

The point where the graph crosses the y-axis is the point that has x-value equal to 0

Checking the graph, we can note that the function crosses the y-axis at only one point which is (0,5)

Part g:

f(x) < 0 means that the output of the function (the y-value) is less than 0 (0 is not included)

Taking a look at the graph, we can note that the function has negative output on the interval from 6 (excluded) to 10 (excluded)

In interval notation, this is written as ]6 , 10[

Part h:

f(-7) means the output of the function (the y-value) at input (x-vale) equal to -7

From the graph, we can note that the function has a constant value of 5 starting from x=5 till -∞

This means that, at x=-7, the value of y is 5 which is a positive value

Hope this helps :)

6 0

4 years ago

Read 2 more answers

This trapezoid has been divided into two right triangles and a rectangle.

Travka [436]

Answer:

Step-by-step explanation:

the area of the rectangle 168 / the triangle on the left is 12/also the triangle on the right is 12/the area of the trapezoid is 192

8 0

2 years ago

What is the length of the shorter of the two chords shown?

krek1111 [17]

Step-by-step explanation:

would you please attach the drawing?????

8 0

3 years ago

Use Properties of Equality 7b+12=5b

Marianna [84]

7b+12=5b

Subtraction property of equality

7b + 12 - 12 = 5b - 12

Simplifying

7b = 5b - 12

Subtraction property of equality

7b - 5b = 5b - 12 - 5b

Simplifying

2b = -12

Division property of equality

2b/2 = -12/2

Simplifying

b = -6

7 0

4 years ago

Read 2 more answers

A person came to work at 8:30 AM, went out at 11:45 AM, had lunch, came in at 12:30 PM, and left work at 5:15 PM. The total numb

Scrat [10]

A person did his first shift from 8:30 AM to 11:45 AM.

The total hours in the morning were:

11 : 45

- 8 : 30

----------

3 : 15

3 hours and 15 minutes.

The second shift was from 12:30 PM to 5:15 PM.

To have the times easier subtracted, assume the final time was 5:30 PM (15 minutes in excess). The total time in the afternoon was:

5:30

- 0:30

----------

5:00

But we have to subtract 15 minutes, thus the total time in the afternoon was

4 hours and 45 minutes.

The total time was 3:15 + 4:45 = 8:00

Answer: 8 hours

4 0

1 year ago