Determine the x-intercept and y-intercepts: y = 2x^2 - 12x + 10

Step 1: Factorize or use the quadratic formula to find the x-intercepts.

y = 2x^2 - 12x + 10 \implies 0 = 2x^2 - 12x + 10

Using the quadratic formula:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

where a = 2 , b = -12 , c = 10 :

x = \frac{12 \pm \sqrt{144 - 80}}{4} = \frac{12 \pm \sqrt{64}}{4} = \frac{12 \pm 8}{4}

x = \frac{12 + 8}{4} = 5 or x = \frac{12 - 8}{4} = 1

So, the x-intercepts are:

\left(1,0\right),\left(5,0\right)

Step 2: Determine the y-intercept by setting x = 0 :

y = 2(0)^2 - 12(0) + 10 = 10

Thus, the y-intercept is:

\left(0,10\right)