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Write an equation for the quadratic graphed below
x-intercepts: (-2,0) and (3,0). y-intercept: (0,-2)

Write An Equation For The Quadratic Graphed Below Xintercepts 20 And 30 Yintercept 02 class=

Sagot :

Sqdancefanidn

Answer:

  y = (1/3)(x +2)(x -3)

Step-by-step explanation:

You want an equation for the quadratic whose graph has x-intercepts (-2, 0) and (3, 0), and y-intercept (0, -2).

X-intercepts

When a polynomial function has a zero at x=q, it means it has a factor of (x -q). Here, the zeros are given as x=-2 and x=3, so the function will have factors ...

  (x -(-2)) = (x +2), and

  (x -3)

Y-intercept

The y-intercept is the constant term in the product ...

  y = a(x +2)(x -3) . . . . . . . product of factors of the quadratic

  y = a(x² -x -6) = ax² -ax -6a

The constant term is -6a, and we want to choose the value of 'a' to make it be -2:

  -6a = -2

  a = -2/-6 = 1/3 . . . . . divide by the coefficient of 'a'

The equation can be written as ...

  y = 1/3(x +2)(x -3)

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