SOLUTION: What are the vertex, the axis of symmetry, the x any y intercepts and the domain and range of the following function? f(x)=2x^2-2x-4

Question 535744: What are the vertex, the axis of symmetry, the x any y intercepts and the domain and range of the following function? f(x)=2x^2-2x-4
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
What are the vertex, the axis of symmetry, the x any y intercepts and the domain and range of the following function? f(x)=2x^2-2x-4
***
y=2x^2-2x-4
complete the square
y=2(x^2-x+1/4)-4-1/2
y=2(x-1/2)^2-9/2
This is an equation of a parabola of standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
For given equation:
lead coefficient>0 means parabola opens upwards and has a minimum
vertex:(1/2, -9/2)
axis of symmetry: x=1/2
..
y-intercept
set x=0
y=-4
x-intercept
set y=0
2(x-1/2)^2-9/2=0
2(x-1/2)^2=9/2
divide by 2
(x-1/2)^2=9/4
take sqrt of both sides
x-1/2=�3/2
x=1/2�3/2
x=2
or
x=-1
..
Domain: (-∞,∞)
Range: (-9/2,∞)
see graph below as a visual check on the answers:

RELATED QUESTIONS
Graph the following the quadratic function give vertex,axis of symmetry domain and range... (answered by lwsshak3)

Graph the function and state the vertex, the axis of symmetry, the intercepts if any.... (answered by lwsshak3)

For the quadratic function : f(x) = 2x^2 - 4x -6, find: a. The x intercepts and the y... (answered by solver91311)

Graph the quadratic function. Indicate the x-intercepts, y-intercepts, domain, range,... (answered by lwsshak3)

Find the domain, range, vertex and axis of symmetry of... (answered by Fombitz)

What are the vertex, axis of symmetry, maximum or minimum value, domain and range for... (answered by TimothyLamb)

Graph the quadratic function. Give the vertex, axis of symmetry, domain, and range.... (answered by oscargut)

Graph the quadratic function. Give the vertex, axis of symmetry, domain, and range.... (answered by solver91311)

Graphing Quadratic Function f(x) = -4x^2 Find the � Direction � Vertex �... (answered by josgarithmetic)