Determine the points of intersection of the function
With the X
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Determine the points of intersection of the function
With the X
To solve this problem, let's determine the points where the function intersects the X-axis.
Step 1: Set the quadratic function equal to zero to find the roots, which represents the X-axis intersection points:
.
Step 2: Consider each factor of the product expression separately:
Set and solve for :
Step 3: Set the second factor equal to zero as well:
Set and solve for :
Step 4: These solutions give us the x-coordinates of the intersection points. Since we set , the points of intersection are
and .
Therefore, the function intersects the X-axis at the points and .
This matches with the choice labeled as choice 2: .
The following function has been graphed below:
\( f(x)=-x^2+5x+6 \)
Calculate points A and B.
The x-axis is where y = 0 everywhere! So any point where the graph touches or crosses the x-axis must have y-coordinate of zero.
If two things multiply to give zero, then at least one of them must be zero. So if , then either or .
No! A quadratic function can have at most 2 x-intercepts. It might have 2 (like this problem), 1 (if it just touches the x-axis), or 0 (if it never crosses).
Look at the coordinates! X-intercepts always have y = 0, like (0,0) and (6,0). Y-intercepts always have x = 0, like (0,5).
No! The factored form is perfect for finding zeros. Expanding to would just make it harder to solve.
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