Consider the parabola f(x) = 5x2 − x − 3. x intercepts

Answer 1

5x^3 -x -3=0

use the quadratic formula

x=-b/2a +/- (1/2a)sqr(b^2-4ac)

x= 1/10 +/- (1/10)sqr(1+60)

x= .1 +/-.1sqr61

x=about .1 +/- .0.781

x=about 0.88 or -0.68

x-intercepts are about x=0.88 or -0.68

about (0.88, 0) and (-0.68, 0)

y=5x^2 -x -3

complete the square, half of 1/5 = 1/10

1/10 squared = 1/100=.01, 5(.01)=.05

y=5(x^2 -x/5) -3

y =5(x^2 -x/5 + 1/100) -3 -0.05

= 5(x-0.1)^2 -3.05

vertex = (.1,-3.05)

x intercepts are equidistant from the x coordinate of the vertex

.88-.1 = .78

|-.68-.1| =.78

x=.1 is the axis of symmetry

Answer 2

(0,-3)

{[(1±sqrt(61))/2],0}