Question

What is the y intercept of the quadratic function f(x)=x^2+x-6

Answer 1

Answer: (0, -6)

Explanation:

got it right on my test

Answer 2

`(0,\, -6)`.

Explanation:

On a cartesian plane, the
`y`-intercept of a function is the point where the graph of that function intersects with the
`y\!`-axis.

The
`y`-axis of a cartesian plane is the same as the equation
`x = 0` (that is, the collection of all points with an
`x`-coordinate of
`0`.)

Construct a system of two equations, with one equation representing
`y`-axis and
`y = f(x)` to represent the graph of this function:

`\begin{aligned}\begin{cases} y = x^(2) + x - 6 & \text{for the quadratic function} \\ x = 0 & \text{for the $y$-axis}\end{cases}\end{aligned}`.

Solve this system for
`x` and for
`y`. If a solution exists, then the
`y\!`-axis and the graph of
`y = f(x)` would indeed intersect. The point
`(x,\, y)` would be the intersection of the
`y\!\!`-axis and the graph of
`y = f(x)\!`.

Substitute the second equation of the system into the first.

`\begin{aligned}\begin{cases} x = 0 \\ y = -6\end{cases}\end{aligned}`.

Hence, the intersection of the
`y`-axis and the graph of
`y = f(x)` would be
`(0,\, -6)`. By definition, this point would be the
`y\!`-intercept of
`y = f(x)\!`.