Write a quadratic equation that has the solutions :4 and -7

Question

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Answer 1

( x - 4 )( x + 7)= 0

x² + 7x - 4x -28 = 0

x² + 3x - 28= 0

Answer 2

If c is a root, then x - c is a factor.

So, an example of a quadratic with roots 4 and -7 is (x-4)(x-(-7)) = (x-4)(x+7) = x² + 3x - 28

Answer 3

x = 4

x-4-0

x=-7

x+7 = 0

(x-4)(x+7) = 0

x^2 +3x -28 =0

f(x) = y = x^2 +3x -28 is a quadratic equation with solutions 4 and -7

It's an upward opening parabola

y=x^2 +3x + 9/4 = 28+ 9/4 is a parabola with vertex (-3/2, -121/4) = minimum point, axis of symmetry x=-3/2

= (x+3/2)^2 = 121/4

(x+3/2) = + or - sqr121/4 = 11/2

x= -3/2 + or - 11/2 = -14/2 or 8/2 = -7 or 4. the solutions are equidistant from the x coordinate of the vertex, -3/2.