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3 years ago

Write in vertex form

Mathematics

1 answer:

nasty-shy [4]3 years ago

5 0

Vertex form: $y=a(x-h)^2+k$

So firstly, put x^2 - 4x into parentheses: $y=(x^2-4x)+6$

Next, we need a perfect square inside the parentheses. Divide the x coefficent by 2 then square that result. In this case, -4 ÷ 2 = -2, (-2)²= 4. Add 4 inside the parentheses and then subtract 4 outside the parentheses:

$y=(x^2-4x+4)+6-4\\y=(x^2-4x+4)+2$

Lastly, factor what's inside the parentheses and your vertex form is $y=(x-2)^2+2$ 

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bazaltina [42]

Answer:

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3 years ago

Graph each function.

artcher [175]

Answer:

Step-by-step explanation:

We can recognize that the parent function for all of these graphs is going to be y=x^2. What this means is that we can graph y=x^2 and then apply transformations to it to get to all of these new graphs.

1. y = -x^2 + 5

We can see that the coefficient of the x^2 term is negative which tells us that the graph will now open downwards.

We also know that we are adding 5 on the outside of the argument which means it affect vertical shift. Therefore, we will be moving 5 units up.

2. y = x^2 - 4

We can see that the only change made to this equation is subtracting 4 on the outside of the squared part of the equation. Again, this signifies vertical movement, but since it's negative we will be moving the entire y = x^2 graph down 4 units.

3. y = -x^2 - 1

What do you notice about this graph?

- negative coefficient

- subtracting 1 outside of the argument

What do these mean?

- negative coefficient: opens downwards

- subtracting 1: move entire y = x^2 graph down 1 unit

7 0

3 years ago

In converting 9 yards to inches, what unit (omit the number) would you place in the numerator of your ratio? Remember that there

mamaluj [8]

Answer:

inches

Step-by-step explanation:

The "to" unit goes in the numerator. (The "from" unit goes in the denominator.) Since we're converting to inches, the numerator of the conversion factor has units of inches.

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9 yd = 9 yd × (36 in)/(1 yd) = 324 in

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4 years ago

Don't know the claim or how to explain

Marrrta [24]

Is this calculus or something?

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3 years ago

The number of students in a class is 60. The number of boys is seven-fifths the number of girls. Find the number of boys in the

Fynjy0 [20]

Step-by-step explanation:

Let the number of girls = x

Therefore, no. of boys = $\frac{7}{5} \times x$

$\because \: no \: of \: boys + no \: of \: girls \: = 60 \\ \\ \therefore \: \frac{7}{5} x + x = 60 \\ \\ \therefore \: \frac{7x + 5x}{5} = 60 \\ \\ \therefore \: \frac{12x}{5} = 60 \\ \\ \therefore \: x = 60 \times \frac{5}{12} \\ \\ \therefore \: x = 5 \times 5 \\ \\ \therefore \: x = 25 \\ \\ \therefore \: \frac{7}{5} x = \frac{7}{5} \times 25 = 7 \times 5 = 35 \\$

Thus, no of boys in the class is 35.

3 0

3 years ago