Calculate Points A and B for the Quadratic Graph of f(x) = x² - 3x - 4

Video Solution

Solution Steps

00:00 Find the coordinates of points A,B

00:03 Notice that points A,B are intersection points with X-axis

00:07 At intersection points with X-axis, Y value must = 0

00:12 Substitute Y = 0 and solve for X values

00:19 Break down the function into a trinomial

00:24 This is the corresponding trinomial

00:30 Find what zeroes each factor in the product

00:34 This is one solution

00:37 This is the second solution

00:46 And this is the solution to the question

Step-by-Step Solution

To solve for points A and B, we find the x-intercepts of the function by setting:

$f(x) = x^2 - 3x - 4 = 0$

We check if it can be factored:

Factor $x^2 - 3x - 4$ . The factors of -4 that add to -3 are -4 and 1.

Thus, factor the function as $(x - 4)(x + 1) = 0$ .

Set each factor to zero:

These are the x-intercepts, or roots, of the quadratic function.

Therefore, the coordinates of points A and B, where the function intersects the x-axis, are $A(-1, 0)$ and $B(4, 0)$ .

The correct choice corresponding to these points is option 3: $A(-1,0), B(4,0)$ .

Thus, the solution to the problem is $A(-1,0), B(4,0)$ .