y=4x^2-16x+12

4(x^2-4x+3)

You can factor this further by seeing which 2 numbers subtract to 4 (your middle term) and add to 3 (your last term). Post if you want it checked/need help.

4[x^2-3x-x+3]

=4[x[x-3)-1(x-3)]
=4[x-1][x-3]

4[x-1][x-3]

The equation you provided is a quadratic equation in the form of y = ax^2 + bx + c, where a = 4, b = -16, and c = 12.

To understand the equation better, let's break down each term:
- The term 4x^2 represents the coefficient of the x^2 term, which means that x is squared in this equation and multiplied by 4.
- The term -16x represents the coefficient of the x term, which means that x is multiplied by -16.
- The term 12 represents the constant term, which is just a number added to the equation.

This quadratic equation represents a parabola when graphed, with specific characteristics such as the vertex, axis of symmetry, and roots/solutions.

To find the vertex of the parabola, you can use the formula:
x = -b / (2a)
y = f(x) = 4x^2 - 16x + 12

Given that a = 4 and b = -16, you can substitute these values into the formula:
x = -(-16) / (2 * 4)
= 16 / 8
= 2

Now, substitute the value of x = 2 into the equation to find the corresponding y-value:
y = 4(2)^2 - 16(2) + 12
= 4(4) - 32 + 12
= 16 - 32 + 12
= -4

Therefore, the vertex of the parabola is (2, -4).

To find the axis of symmetry, you simply take the x-value of the vertex. So in this case, the axis of symmetry is x = 2.

To find the roots or solutions of the quadratic equation, you can use factoring, completing the square, or the quadratic formula. However, this equation doesn't easily factor, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the given values of a = 4, b = -16, and c = 12 into the formula, we have:
x = (-(-16) ± √((-16)^2 - 4*4*12)) / (2*4)
= (16 ± √(256 - 192)) / 8
= (16 ± √64) / 8
= (16 ± 8) / 8

Now we have two possible solutions:
x1 = (16 + 8) / 8
= 24 / 8
= 3

x2 = (16 - 8) / 8
= 8 / 8
= 1

Therefore, the two roots or solutions to the equation are x = 3 and x = 1.