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kenny6666 [7]
2 years ago
5

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

Mathematics
1 answer:
saveliy_v [14]2 years ago
4 0

Answer:

(0,\, -6).

Step-by-step 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)\!.

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