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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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Step-by-step explanation:

Simplify the following:

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Hint: | Distribute 7 over x - 4.

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Hint: | Group like terms in 7 x - 3 x - 28 - 15.

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Hint: | Evaluate -28 - 15.

-28 - 15 = -43:

Answer: 4 x + -43

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