Question

What is the vertex of `y=3x^2-7x+12`? What are its x-intercepts?

Answer 1

Find vertex of `y = 3x^2 - 7x + 12`.

Explanation:

x-coordinate of vertex:
`x = (-b/(2a)) = 7/6`
y-coordinate of vertex:
`y = y(7/6) = 3(49/36) - 7(7/6) = 12 = 147/36 - 49/6 + 12 =`
`= - 147/36 + 432/36 = 285/36 = 7.92`
Vertex `(7/6, 7.92)`
To find the 2 x-intercepts, solve the quadratic equation:
`y = 3x^2 - 7x + 12 = 0.`
`D = b^2 - 4ac = 49 - 144 < 0`. There are no x-intercepts. The parabola opens upward and is completely above the x-axis.
graph{3x^2 - 7x + 12 [-40, 40, -20, 20]}