What Are the X-Intercepts of a Parabola?

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To find the x-intercepts of the parabola defined by the equation y = (x + 2)² - 3, set y to zero and solve for x. This involves solving the equation (x + 2)² - 3 = 0. Understanding the definitions of x-intercepts and y-intercepts is crucial for solving such problems. The x-intercepts represent the points where the parabola crosses the x-axis. Clarifying these concepts can help in approaching similar mathematical problems effectively.
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Homework Statement


Identify the x-intercept(s) of the parabola y = (x + 2)2 – 3


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The Attempt at a Solution


No idea on where to begin and if I would do the same thing with y
 
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to find the y intercepts, let x=0,
so to find the x intercepts let what=0?
 
When you have "no idea where to begin" you probably don't understand some of words in the problem. In a case like that it is always a good idea to review the definitions: what do "x-intercept" and "y-intercept" mean?
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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