Question

Find the y-int, the axis of symmetry, and the vertex of the graph of the function. f(x) = -2x^2 + 4x - 6

Answer 1

Given the function f(x) = -2x²+4x-6, we can find the vertex using the following general expression:

`(-(b)/(2a),f(-(b)/(2a)))`

where a and b are the main coefficients on the quadratic function. In this case, we have that a = -2 an b = 4, then:

`\begin{gathered} -(b)/(2a)=-(4)/(2(-2))=-(4)/(-4)=1 \\ \Rightarrow f(1)=-2(1)+4(1)-6=-2+4-6=-8+4=-4 \end{gathered}`

thus, the vertex is the point (1,-4).

The y-intercept can be found by evaluating x = 0 on the functions, then, we have the following:

`\begin{gathered} x=0 \\ \Rightarrow f(0)=-2(0)+4(0)-6=-6 \end{gathered}`

so, the y-intercept is the point (0,-6).

Finally, the axis of symmetry will be the line that divides in two equal pieces the parabola, this happens on the x component of the vertex, then, the axis of symmetry is the line x = 1