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professor190 [17]
2 years ago
10

Explain how to factor when the leading coefficient is 1.

Mathematics
1 answer:
Bas_tet [7]2 years ago
3 0

Answer:  C) Find the factors of c that add up to b.

==============================================

Explanation:

If we want to factor something in the form x^2+bx+c, then we look for two numbers that

  • Multiply to c
  • Add to b

-------------

Let's look at a specific example

Consider factoring x^2+5x+6

We need to find two numbers that...

  • Multiply to c = 6
  • Add to b = 5

Through trial and error, you should find the two numbers to be 3 and 2. This means it factors to (x+3)(x+2). The order of the factors doesn't matter.

You can use the FOIL rule or the box method to expand out (x+3)(x+2). You should get x^2+5x+6 again.

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A parabola can be drawn given a focus of
Volgvan

Answer:

y=-\frac{1}{4}(x-2)^{2}+9

Step-by-step explanation:

Any point on a given parabola is equidistant from focus and directrix.

Given:

Focus of the parabola is at (2,8).

Directrix of the parabola is y=10.

Let (x,y) be any point on the parabola. Then, from the definition of a parabola,

Distance of (x,y) from focus = Distance of (x,y) from directrix.

Therefore,

\sqrt{(x-2)^{2}+(y-8)^{2}}=|y-10|

Squaring both sides, we get

(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9

Hence, the equation of the parabola is y=-\frac{1}{4}(x-2)^{2}+9.

4 0
3 years ago
5/4 = equals what like I need an answer
defon

In decimal form, 5/4 is equal to 1.25

5 0
3 years ago
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Your translation is "to solve or decide" hope this helps!
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