Graph a parabola whose x-intercepts are at x = -6 and x = 2 and whose minimum value is -8.
Graph a parabola whose x-intercepts are at x = -6 and x = 2 and whose minimum value is -8.
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info@snapandsolve.comThe equation of a parabola with x-intercepts at x = -6 and x = 2 can be written in factored form as:
y = a(x + 6)(x - 2)
To find the value of 'a', use the given minimum value of the parabola, which is -8. The vertex of the parabola is the midpoint of the x-intercepts, which is x = (-6 + 2) / 2 = -2. Substitute x = -2 and y = -8 into the equation:
-8 = a(-2 + 6)(-2 - 2)
-8 = a(4)(-4)
-8 = -16a
a = 1/2
Thus, the equation of the parabola is:
y = (1/2)(x + 6)(x - 2)
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