Algebra 1 Question

Question

What equation do you use to solve this equation solving by factoring and the zero product property?

x²+5x-24=12

Solve the equation:

 x²+5x-24=12

Answer 1

x^2 +5x -24 = 12 subtract 12 from both sides

x^2 +5x -36 = 0 factor

(x+9)(x-4) = 0 set each factor = 0

x+9=0, x-4 = 0

x=-9 or 4

If you graphed it, you'd have an upward opening parabola with x intercepts -9 and 4

the axis of symmetry would be the average of the x intercepts (-9+4)/2 = -2.5 = x which is also the x coordinate of the vertex

x^2 +5x -36 = 0 is in ax^2 +bx + c form where a=1, b=5, c=-36

axis of symmetry is x= -b/2a = -5/2 = -2.5

y intercept = c =-36

complete the square to find the vertex

x^2 +5x + 25/4 -36 - 35/4 = 0

(x+5/2)^2 - 179/4 = 0

vertex of the parabola is (5/2, -179/4) = (2.5, - 44.75)