what is the axis of summetry and vertex and yint and xint of -x^2+2x+15
We have y = f(x) = -x^2 + 2x + 15
y = -(x^2 - 2x - 15)
y = - (x - 5)(x + 3)
y = 0 at x = 5 and at x = -3
The x intercepts are: x = 5, x = -3
When x = 0, y = -(-5)(3) = 15
The y intercept is: y = 15
The axis od symmetry is the vertical line that passes through the highest point on the graph.
This highest point is at a turning point on the graph. i.e. when the slope (i.e. dy/dx) of the graph is zero.
y = -x^2 + 2x + 15
dy/dx = -2x + 2
when dy/dx = 0, x = 1
x = 1 represents a vertical line passing through the x-axis at x = 1.
The axis of symmetry is: x = 1