what are the solutions of y=−x^2−4x+7

Answer 1

y = -x^2 -4x + 7, set = zero and multiply by -1

x^2 +4x -7 =0

x^2 +4x = 7 complete the square or use the quadratic formula, if it doesn't factor

= x^2 +4x + 4 = 7 +4 take half the x coefficient and square it, then add 4 to both sides

(x+2)^2 = 11 take square roots of both sides

x+2 =+ or - sqr11 subtract 2 from both sides

x= -2 + or - sqr11 = about 1,3 or - 5.3 square root of 11 is about 3.3

if you graph the equation, it will intersect the x axis at about (1.3, 0) and (-5.3, 0)

It's a downward opening parabola with axis of symmetry x=-2

vertex and maximum point (-2, 11)

y intercept (0,7)

x intercepts about (1.3, 0) and (-5.3, 0)

IF you graphed it, where the curve intersects the x axis are the two solutions to the equation.