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stellarik [79]
3 years ago
12

I need help bruv. For the function y=x^2 - 5x - 6 .

Mathematics
1 answer:
lara [203]3 years ago
4 0

Answer:

a. Vertex = (2.5,-12.25)

b. y-intercept = (0,-6)

c. x-intercept = (6,0) ; (-1,0)

Step-by-step explanation:

a.

Your equation is written as:

y = ax^{2} + bx +c

The easiest way to find the vertex is writing the equation this way:

y = a(x-h)^{2}+k

Being the vertex (h,k)

So first complete the square

y = x^{2} -5x -6 \\y = x^{2} - 2(2.5x) -6 \\y = x^{2} - 2(2.5x) +2.5^{2} - 2.5^{2} -6 \\y = (x^{2} -2(2.5x) + 2.5^{2}) -6.25 - 6 \\y = (x-2.5)^{2} -12.25

Vertex : (2.5,-12.25)

b.

To find the y-intercept you need to replace the equation when x = 0 and get y

y = (0)^{2} - 5(0) -6\\y = - 6

c.

To find the x-intercept you need to replace the equation when y = 0 and get x

0 = x^{2} - 5x -6 \\0 = (x-6)(x+1)\\x = 6\\x = -1

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The length of a rectangle is 3 more than 3 times its width. The perimeter of the rectangle is 174 inches. What is the length of
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Answer:

<em>l = w + 3cm</em>

<em>l = w + 3cmp = 2l + 2w = 58cm</em>

<em>l = w + 3cmp = 2l + 2w = 58cm </em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 </em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:l = (13cm) + 3cm = 16cm</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:l = (13cm) + 3cm = 16cmStep-by-step explanation:</em>

I hope this helps you.

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3 years ago
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