You can find it by taking the derivative of the function and solving for zero:
y = -4x2 - 24x - 29
∴ y' = -8x - 24
Let y' = 0:
0 = -8x - 24
8x = -24
x = -3
Now you can plug that x value into the original equation to get it's corresponding y co-ordinate:
y = 4(-3)2 - 24(-3) - 29
∴ y = 27 + 72 - 29
∴ y = 70
So the vertex is at the point {-3, 70}
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First, factor it out. This would first look like x(24x-29)=0, which would mean that x=0 or 29/24.
The idea is to solve the equation -3x2 + 24x - 19 = 0. You can use the quadratic formula for this, using a = -3, b = 24, c = 19. Or complete the square since dividing by -3 will give us 8x, an even coefficient. -3x2 + 24x - 19 = 0 (add and subtract 48 to the left side) -3x2 + 24x -48 + 29 = 0 (subtract 29 to both sides, and factor out -3) -3(x2 - 8x + 16) = -29 (divide by -3 to both sides) (x - 4)2 = 29/3 x - 4 = ± √(29/3) (add 4 to both sides) x = 4 ± √(29/3) (multiply by 3/3 inside the radical, if you want to rationalize the denominator) x = 4 ± (√87)/3
if you mean 6-5c=-29:c=7
5 times 2 square equals 20 minus 29 equals -9
29