Answer:
The y-intercept is -2
The equation of the axis of symmetry is x = 1
Explanation:
* Lets revise the general form of the quadratic function
- The general form of the quadratic function is f(x) = ax² + bx + c,
where a, b , c are constant
# a is the coefficient of x²
# b is the coefficient of x
# c is the y-intercept
- The meaning of y-intercept is the graph of the function intersects
the y-axis at point (0 , c)
- The axis of symmetry of the function is a vertical line
(parallel to the y-axis) and passing through the vertex of the curve
- We can find the vertex (h , k) of the curve from a and b, where
h is the x-coordinate of the vertex and k is the y-coordinate of it
# h = -b/a and k = f(h)
- The equation of any vertical line is x = constant
- The axis of symmetry of the quadratic function passing through
the vertex then its equation is x = h
* Now lets solve the problem
∵ f(x) = -2x² + 4x - 2
∴ a = -2 , b = 4 , c = -2
∵ The y-intercept is c
∴ The y-intercept is -2
∵ h = -b/2a
∴ h = -4/2(-2) = -4/-4 = 1
∴ The equation of the axis of symmetry is x = 1