Question

Consider the quadratic function f(x) = –2x2 + 4x – 2. Find the y-intercept and the equation of the axis of symmetry.

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = - 2x² + 4x - 2

To find the y- intercept set x = 0

f(0) = 0 + 0 - 2 = - 2 ← y- intercept

The equation of the axis of symmetry is of the form x = c

where c is the value of the x- coordinate the line goes through.

Given the equation in standard form

with a = - 2, b = 4 then the axis of symmetry is

x = - $\frac{b}{2a}$ = - $\frac{4}{-4}$ = 1

Equation of axis of symmetry is x = 1

Answer 2

Answer:

The y-intercept is -2

The equation of the axis of symmetry is x = 1

Step-by-step 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