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Lana71 [14]
2 years ago
15

Rewrite the quadratic function in vertex form. Y=2x^2+4x-1

Mathematics
1 answer:
Fantom [35]2 years ago
5 0

Answer:

\large\boxed{y=2(x+1)^2-3}

Step-by-step explanation:

The vertex form of an equation of a parabola:

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

(h, k) - vertex

We have

y=2x^2+4x-1=2\left(x^2+2x-\dfrac{1}{2}\right)

We must use the formula: (a+b)^2=a^2+2ab+b^2\qquad(*)

2\left(x^2+2(x)(1)-\dfrac{1}{2}\right)=2\bigg(\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-\dfrac{1}{2}\bigg)\\\\=2\left((x+1)^2-1-\dfrac{1}{2}\right)=2\left((x+1)^2-\dfrac{3}{2}\right)

Use the distributive formula a(b + c) = ab + ac

2(x+1)^2+2\left(-\dfrac{3}{2}\right)=2(x+1)^2-3

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A new shopping mall records 120 total shoppers on their first day of business. Each day after that, the number of shoppers is 10
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Answer:

1,139\ shoppers

Step-by-step explanation:

we know that

In this problem we have a exponential function of the form

y=a(b)^{x}

where

a is the initial value or y-intercept

b is the base of the exponential function

r is the rate in decimal form

b=(1+r)

In this problem we have

x ----> the number of days

y ----> the number of shoppers

a=120

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b=1+0.10=1.10

substitute the values

y=120(1.10)^{x}

First day

y=120

Second day

For x=1 day

substitute the value of x in the equation and solve for y

y=120(1.10)^{1}=132

Third day

For x=2 days

y=120(1.10)^{2}=145

Fourth day

For x=3 days

y=120(1.10)^{3}=160

Fifth day

For x=4 days

y=120(1.10)^{4}=176

Sixth day

For x=5 days

y=120(1.10)^{5}=193

Seventh day

For x=6 days

y=120(1.10)^{6}=213

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