The problem asks us to find the x-intercepts and y-intercept of the quadratic function $f(x) = -x^2 + x + 6$. We need to give the intercepts as coordinate points $(x, y)$.

1. Problem Description

The problem asks us to find the x-intercepts and y-intercept of the quadratic function $f(x) = -x^2 + x + 6$. We need to give the intercepts as coordinate points $(x, y)$.

2. Solution Steps

First, let's find the x-intercepts. The x-intercepts are the points where the function $f(x)$ is equal to zero. So we need to solve the equation $-x^2 + x + 6 = 0$.

Multiply by -1 to make leading coefficient positive:

$x^2 - x - 6 = 0$

We can factor the quadratic expression:

$(x - 3)(x + 2) = 0$

This gives us two solutions for x:

$x - 3 = 0$ or $x + 2 = 0$

$x = 3$ or $x = -2$

Therefore, the x-intercepts are $x = 3$ and $x = -2$.

Since $x = -2$ is smaller than $x = 3$, the smaller x-intercept is $(-2, 0)$ and the larger x-intercept is $(3, 0)$.

Next, let's find the y-intercept. The y-intercept is the point where $x = 0$. We can find it by evaluating $f(0)$.

$f(0) = -(0)^2 + (0) + 6 = 6$

Therefore, the y-intercept is at $y = 6$. The coordinate point is $(0, 6)$.

3. Final Answer

The smaller x-intercept is the point: (-2, 0)

The larger x-intercept is the point: (3, 0)

The y-intercept is the point: (0, 6)