What are the x-intercepts of the parabola represented by the equation y = 3x2 + 6x − 10

x ≈ {-3.082, 1.082}

I find the easiest way to answer such a question (with medium accuracy) is to use a graphing calculator. The graph shown in the attachment gives the answers listed above.

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From vertex form

The graphing calculator also makes it easy to find the vertex of the parabola. If we divide by 3 so the scale factor is 1, then the y-value of the vertex is -13/3 and the vertex form of the equation can be written ...

... y = (x +1)² -13/3

This has x-intercepts easily found.

... 0 = (x +1)² -13/3 . . . . x-intercepts are where y=0

... (x +1)² = 13/3 . . . . . . . add 13/3

... x +1 = ±√(13/3) . . . . . take the square root

... x = -1 ±√(13/3) . . . . . subtract 1

... x ≈ {-3.0816660, 1.0816660}

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Using the quadratic formula

This equation has a=3, b=6, c=-10, so we can put these values into the quadratic formula to find the x-interecepts.

... x = (-b±√(b²-4ac))/(2a)

... x = (-6 ±√(6² -4(3)(-10)))/(2(3))

... x = (-6 ±√156)/6 = -1 ±√(13/3) . . .  or . . . -1 ±(√39)/3

the solution is h=10 because you add 9 to each side of the equation.