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Pani-rosa [81]
3 years ago
6

A quadratic equation that has X-intercepts of (-2,0) and (8,0), a stretch of 3, and the vertex is a minimum.

Mathematics
1 answer:
umka21 [38]3 years ago
7 0

Answer:

a. y = 3 × (x + 2)(x - 8)

b.  y = 3·(x - 3)² - 75

c) y =  3·x² - 18·x - 48

Step-by-step explanation:

The x-intercept of the quadratic equation are (-2, 0), (8, 0)

The stretch of the quadratic equation = 3

We have;

a. The factored form y = 3 × (x + 2)(x - 8)

b. From the vertex form, we have;

y = 3 × (x + 2)(x - 8) = 3·x² - 18·x - 48

y = 3·x² - 18·x - 48

The vertex form a(x - h)² + k

Where;

h = -b/(2·a) = 18/6 = 3

h = 3

k = c - b²/(4·a) = -48 - (18²)/12 = -75

The vertex form 3·(x - 3)² - 75

c) The standard form of the quadratic equation, y = a·x² + b·x + c

The standard form of the quadratic equation is y =  3·x² - 18·x - 48.

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Explanation:

As points have three coordinates i.e. x, y and z hence the sketch of the given four points is drawn in 3D shape and for that picture is attached here with this answer.

Points are given in the format as below

(value of x-coordinate , value of y-coordinate , value of z-coordinate)

In the attachment:

Point A = (0,5,2) (in blue color)

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Answer:

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