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3 years ago

What is the vertex of the equation, y= -3x^2+2x-7?

Mathematics

2 answers:

Genrish500 [490]3 years ago

4 0

Given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 ), then

The x-coordinate of the vertex is

$x_{vertex}$ = - $\frac{b}{2a}$

y = - 3x² + 2x - 7 is in standard form

with a = - 3, b = 2 and c = - 7, hence

$x_{vertex}$ = - $\frac{2}{-6}$ = $\frac{1}{3}$

Substitute this value into the equation for y-coordinate

y = - 3 ( $\frac{1}{3}$ )² + 2 ( $\frac{1}{3}$ ) - 7

= - $\frac{1}{3}$ + $\frac{2}{3}$ - $\frac{21}{3}$ = - $\frac{20}{3}$

vertex = ( $\frac{1}{3}$ , - $\frac{20}{3}$ ) → A

Alex17521 [72]3 years ago

3 0

1) with this formula you can calculate the value of x , x = -b/2a

2) substitute the values x = -(2)/2(-3) = 2/6 = 1/3

3) substitute the value of x in the function

y= -(3)(1/3)^2+(2*1/3)-7 = -20/ 3, therefore , the correct option is A

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Answer:

Step-by-step explanation:

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NOTES:

Use the equation y = mx + b where m is the unit rate and b is the one-time flat fee

1. Answer:

$\begin {array}{c||c|c|c|c}x&0&1&2&3\\ y&70.00&70.20&70.40&70.60\\\end{array}$

Step-by-step explanation:

coffee maker costs $70 - this is a one-time flat fee

it costs $0.20 per cup of coffee - this is the unit rate

y = 0.20x + 70

y = 0.20(0) + 70 → y = 0.00 + 70 → y = 70.00

y = 0.20(1) + 70 → y = 0.20 + 70 → y = 70.20

y = 0.20(2) + 70 → y = 0.40 + 70 → y = 70.40

y = 0.20(3) + 70 → y = 0.60 + 70 → y = 70.40

*******************************************************************************

2. Answer:

$\begin {array}{c||c|c|c|c}x&1&2&3&4\\ y&4.50&6.00&7.50&9.00\\\end{array}$

Step-by-step explanation:

shoes costs $3.00 - this is a one-time flat fee

it costs $1.50 per game of bowling - this is the unit rate

y = 1.50x + 3.00

y = 1.50(1) + 3.00 → y = 1.50 + 3.00 → y = 4.50

y = 1.50(2) + 3.00 → y = 3.00 + 3.00 → y = 6.00

y = 1.50(3) + 3.00 → y = 4.50 + 3.00 → y = 7.50

y = 1.50(4) + 3.00 → y = 6.00 + 3.00 → y = 9.00

*******************************************************************************

3. Answer: Negative

Step-by-step explanation:

As the x-values increase, the y-values decrease. Opposite directions results in a negative slope.

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4. Answer: Gym A → y = 20x + 50 Gym B → y = 25x + 30

Step-by-step explanation:

Use the slope formula: $m = \dfrac{y_2-y_1}{x_2-x_1}$ . Then choose ONE of the points and input the point (x₁, y₁) and slope (m) into the Point-Slope formula: y - y₁ = m(x - x₁) and solve for y.

Gym A: (x₁, y₁) = (1, 70) and (x₂, y₂) = (2, 90)

$m=\dfrac{90-70}{2-1} = \dfrac{20}{1} = 20$

y - 70 = 20(x - 1)

y - 70 = 20x - 20

y = 20x + 50

Gym B: (x₁, y₁) = (1, 55) and (x₂, y₂) = (2, 80)

$m=\dfrac{80-55}{2-1} = \dfrac{25}{1} = 25$

y - 55 = 25(x - 1)

y - 55 = 25x - 25

y = 25x + 30

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3 years ago

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makkiz [27]

Answer:

The answer is the third equation. A = 250*(1 +0.016)^(0.75)

Step-by-step explanation:

Since Javier deposited $250 into an account with annual interest rate, then as the years passes his account will grow in the manner shown below:

account(0) = 250

account(1) = account(0)*(1 + 1.6/100) = account(0)*(1 + 0.016) = account(0)*1.016

account(2) = account(1)*1.016 = account(0)*1.016*1.016 = account(0)*(1.016)²

account(3) = account(2)*1.016 = account(0)*(1.016)²*1.016 = account(0)*(1.016)³

account(n) = account(0)*(1.016)^n

Where n is the number of years, account(0) is the initial amount. In this case only 9 months have passed, so we need to convert this value to years, dividing it by 12, which is 9/12 = 0.75. The initial amount was 250, so the equation is:

A = 250*(1.016)^(0.75)

The answer is the third equation.

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3 years ago

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