 Solve each equation. If exact roots cannot be found, state the consecutive integers between which the roots are located

Question

X^2-6x+5=0

solve it and graph it please.

Answer 1

(x-5)(x-1) = 0

x=1,5 = 2 roots, zeroes or x-intercepts or the points (1,0) and (5,0) both on the x axis to the right of the origin

x^2-6x+5 =0

x^2 -6x + 9 = -5+9 = 4

(x-3)^2 = 4

x-3 = + or - 2

x= 3+ or - 2 = 1 or 5 = 2 roots

axis of symmetry is the average (1+5)/2 = 3, x=3 is the axis of symmetry, and the vertex has an x coordinate = 3. the y intercept = 5 found by setting x=0 y=(0)^2 -6(0) +5 = 5 that's the point (0,5). Also another point on the parabola, due to symmetry is (6,5)

y = 3^2 -6(3) + 5 = 9-18+5 =-4 = the y coordinate of the vertex. The vertex is (3,-4)

plot the two x intercepts, the y intercept, the symmetrical point and the vertex and draw a smooth parabola through those points. It's an upward opening parabola with minimum point at the vertex (3,-4)