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 find the points of intersection with the x-axis for the function , we must determine when .
Using the zero-product property, set each factor equal to zero separately:
Solving the first equation, :
Add 1 to both sides:
.
Solving the second equation, :
Subtract 1 from both sides:
.
Divide both sides by 2:
.
The solutions are the x-intercepts of the function. Therefore, the points of intersection are and .
Thus, the points of intersection on the x-axis are and .
The following function has been graphed below:
\( f(x)=-x^2+5x+6 \)
Calculate points A and B.
X-intercepts are points where the graph crosses the x-axis, meaning the y-coordinate is always 0. So you're looking for values of x where y = 0.
You'll need to factor it first! Look for two numbers that multiply to give the constant term and add to give the middle coefficient, or use the quadratic formula.
No! A quadratic function can have at most 2 x-intercepts. It might have exactly 2 (like this problem), exactly 1, or none at all.
X-intercepts are always written as (x-value, 0). Since they're on the x-axis, the y-coordinate is always zero. So becomes .
It means that if you multiply two or more numbers and get zero, at least one of those numbers must be zero. It's impossible to multiply non-zero numbers and get zero!
No! Keep it factored - that's the whole advantage! Expanding to just makes the problem harder.
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