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Tasya [4]
3 years ago
15

What is the vertex of the parabola

Mathematics
1 answer:
katovenus [111]3 years ago
6 0

Let's consider the equation of parabola, y = a·(x - α)·(x - β)

where α, β are the x-intercepts.

From the given graph, the y-intercept is (0, -3).

From the given graph, the x-intercept are (-1, 0) and (3, 0) i.e. α = -1, β = 3.

So the equation of parabola would be now, y = a·(x + 1)·(x - 3)

We can plug the y-intercept (0, -3) in the equation to find value of 'a'.

-3 = a·(0+1)·(0-3)

-3 = -3a

a = 1

So the equation of parabola would be now, y = (x + 1)·(x - 3) = x² - 2x - 3

Comparing it with y = ax² + bx + c

The x-coordinate of vertex would be, x = \frac{-b}{2a} = \frac{-(-2)}{2(1)} =\frac{2}{2} = 1

the y-coordinate of vertex would be, y = (1)² - 2(1) - 3 = -4.

Hence, vertex would be (1, -4).

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2 years ago
Dominic pays 7% interest on his $16,000 college loan and 12% interest on his $12,000 car loan. What average interest rate does h
Naya [18.7K]

The average interest rate is 8.57% paid on the total of $28,000

<h3>What is the percentage?</h3>

The percentage is defined as a ratio expressed as a fraction of 100.

Dominic pays 7% interest on his $16,000 college loan,

And 12% interest on his $12,000 car loan

To determine the average interest rate paid on the total $28,000 he owes

Calculating the total interest amount paid :

⇒ 7% of 16,000 +  12% of 12,000

⇒ (7/100)16,000 +  (12/100)12,000

⇒ (0.07)16,000 +  (0.12)12,000

⇒ (0.07)16,000 +  (0.12)12,000

⇒ 960 + 1440

⇒ 2400

So the average interest rate paid on the total of $28,000 as

⇒ 2400/28,000 = 0.0857 ≈ 8.57%

Hence, the average interest rate is 8.57% paid on the total of $28,000

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1 year ago
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Step-by-step explanation:

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