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fomenos
3 years ago
13

Please help if you can!

Mathematics
1 answer:
marin [14]3 years ago
6 0

9514 1404 393

Answer:

  y = 1/2x^2 +x -15/2

Step-by-step explanation:

The vertex is the point where the graph reaches is extreme: (-1, -8). The y-intercept is (0, -7.5). The x-intercepts are (-5, 0) and (3, 0).

When the quadratic is written in the form ...

  y = x^2 +bx +c

the value of b is the opposite of the sum of the x-intercepts. The value of c is their product. These facts would give ...

  y = x^2 -(-5 +3)x +(-5)(3) = x^2 +2x -15

The constant in this equation is -15, which is the value y has when x=0. Our actual y-intercept is half that, so the graph we see is this equation scaled by a factor of 1/2:

  y = 1/2x^2 +x -15/2

_____

<em>Alternate solution</em>

You can start with the vertex form.

  y = a(x -h)^2 +k . . . . . . . vertical scale factor 'a' and vertex (h, k)

On the graph, the vertical scale factor is the vertical difference between the low point (vertex) and the point that is 1 unit right or left. Here, that is ...

  -7.5 - (-8) = 0.5 = a

We've already said the vertex is (h, k) = (-1, -8), so the vertex form equation is ...

  y = 0.5(x +1)^2 -8

We know the square of a binomial is (a+b)^2 = a^2 +2ab +b^2, so we have ...

  y = 0.5(x^2 +2x +1) -8

  y = 0.5x^2 +x +0.5 -8 . . . . . eliminate parentheses

  y = 0.5x^2 +x -7.5

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7 0
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Read 2 more answers
Let f(x)=5(x^2-3)+10. which statement must be true?
Maslowich
Find where the expression
x
−
5
x
2
−
25
x
-
5
x
2
-
25
is undefined.
x
=
−
5
,
x
=
5
x
=
-
5
,
x
=
5
Since
x
−
5
x
2
−
25
x
-
5
x
2
-
25
→
→
−
∞
-
∞
as
x
x
→
→
−
5
-
5
from the left and
x
−
5
x
2
−
25
x
-
5
x
2
-
25
→
→
∞
∞
as
x
x
→
→
−
5
-
5
from the right, then
x
=
−
5
x
=
-
5
is a vertical asymptote.
x
=
−
5
x
=
-
5
Consider the rational function
R
(
x
)
=
a
x
n
b
x
m
R
(
x
)
=
a
x
n
b
x
m
where
n
n
is the degree of the numerator and
m
m
is the degree of the denominator.
1. If
n
<
m
n
<
m
, then the x-axis,
y
=
0
y
=
0
, is the horizontal asymptote.
2. If
n
=
m
n
=
m
, then the horizontal asymptote is the line
y
=
a
b
y
=
a
b
.
3. If
n
>
m
n
>
m
, then there is no horizontal asymptote (there is an oblique asymptote).
Find
n
n
and
m
m
.
n
=
1
n
=
1
m
=
2
m
=
2
Since
n
<
m
n
<
m
, the x-axis,
y
=
0
y
=
0
, is the horizontal asymptote.
y
=
0
y
=
0
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes:
x
=
−
5
x
=
-
5
Horizontal Asymptotes:
y
=
0
y
=
0
No Oblique Asymptotes
5 0
3 years ago
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