what is the graph of equation y=2x-4x^2 ?
Answers
graph equation y=2x-4x^2
Answer:
The equation y=2x−4x2 represents a parabola. Our goal should be to bring this equation to the standard form:
(x−h)2=4a(y−k)(1)
Here, (h,k) are the coordinates of the vertex of a parabola.
We start with:
y=2x−4x2
⟹y4=x2−x2
⟹−y4=x2−x2
Complete the square on the RHS:
−y4=(x2−x2+(116))−(116)
−y4=(x−14)2−(116)
(116)+−y4=(x−14)2
⟹(x−14)2=4(−116)(y−14)(2)
Comparing above equation with (1), we get:
h=14
k=14
Equation (2) can be converted to a simpler form by shifting the origin of the coordinate system to the vertex of the parabola itself yielding:
X2=4(−116)Y(3)
Where, X=x−14 and Y=y−14. Comparing (3) with X2=4(−a)y, we conclude that (3), and hence (2) represents a downward opening parabola having its vertex at (14,14). Setting y=0, we also observe that this parabola intersects the x-axis at the origin and at the point (0.5,0). So the parabola would look like this:
