what is the x and y incercepts of y=(5x-1)(x+1)

Question

x and y intercepts, prove its symmetry, and graph

Answer 1

To find x-intercepts, plug in y=0, so 5x-1=0 and x+1=0 for the x-intercepts, that is, x=⅕ and x=-1⇒(⅕,0) and (-1,0).

To find y intercept, plug in x=0, so y=-1 is the y-intercept (0,-1).

To draw the graph it would be helpful to find the vertex which also gives us the axis of symmetry of the quadratic.

y=5x²+4x-1=5(x²+⅘x)-1, now complete the square:

y=5(x²+⅘x+4/25)-⅘-1=5(x+⅖)²-9/5 or 5(x+0.4)²-1.8. This tells us that the vertex is (-0.4,-1.8) and the axis of symmetry is x=-0.4.

The vertical blue line is the axis of symmetry (passing through the vertex). There's one y-intercept and two x-intercepts.