Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the following function.
y=-4x^2−24x−31
The axis of symmetry is x =
The vertex is
To find the axis of symmetry, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form (by moving all terms to one side). In this case, the quadratic equation is y = -4x^2 - 24x - 31, so a = -4 and b = -24.
Using the formula x = -b/2a, we have x = -(-24)/2(-4) = 24/8 = 3.
Therefore, the axis of symmetry is x = 3.
To find the coordinates of the vertex, we substitute the x-value from the axis of symmetry into the original equation.
Using x = 3, we have y = -4*(3)^2 - 24*(3) - 31 = -36 - 72 - 31 = -139.
So the vertex is (3, -139).