We will start by identifying the values of a, b, and c.
f(x)=2x^2-12x+6 ⇕ f(x)=2x^2+( - 12)x+ 6We can see that a = 2, b = - 12, and c = 6. Since the y-intercept is given by the value of c, we know that the y-intercept is 6. Let's now substitute a=2 and b=- 12 into - b2a to find the axis of symmetry.
The equation of the axis of symmetry is x=3.
To find the vertex of the parabola, we will need to think of y as a function of x, y=f(x). We can write the expression for the vertex by stating the x- and y-coordinates in terms of a and b.
Vertex: ( - b/2a, f(- b/2a ) )
When determining the axis of symmetry, we found that - b2a=3. Therefore, the x-coordinate of the vertex is 3 and the y-coordinate is f(3). To find this value, substitute our x-coordinate for x in the given equation.
