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Is the only way to solve this question to substitute points or THERES some other way?
welistenforyou
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Jun 21, 2022
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Is the only way to solve this question to substitute points or THERES some other way?
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welistenforyou
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Jun 21, 2022
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First, the coefficient of x^2 is negative, which means the parabola opens downwards, eliminating D. Second, the constant term is the y-intercept. The only one left that passes through (0, 1) is C.
balde_ibrahima
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Jun 21, 2022
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When you have a parabola with the equation
y = Ax² + Bx + C
Then each of the three parameters have a specific meaning
C = y-coordinate of intersection with the y-axis
B = slope of curve when it intersects the y-axis (rarely mentioned)
A = height difference between vertex and the points Δx=1 next to it
positive if the parabola opens upwards, negative if it opens downwards
With these in mind, which parabola fits?
MCSeto
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Jun 21, 2022
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MCSeto
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You could absolutely use substitution, but I think it would be a waste of your time. A better question is, what each variable in the equation stands for.
Ax^2 + Box + C
The first one I look for is C; the y-intercept.
B is the slope at the y intercept
Based on this, you can safely say that C is the right answer
IB_DP
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Jun 21, 2022
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IB_DP
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You can also rewrite the function (now) general form into the vertex form y = a(x - p)² + q and then the vertex should be (p,q)
rorydcarroll
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Jun 21, 2022
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Well substitution is by far the easiest (for example x=0 and x=-1 narrows it down to c un this case, those are not hard to compute, or if you happen to know that the direction of the parabola depends on the sign of the coefficient of x^2 than just x=0 is enough).
There are a lot of other methods though (many of which have been mentioned already):
You can look at where the function intersects the axes
You can look at it's derivative, find its slope at certain points
You can look for its roots with the quadratic formula
You can look for the roots of its derivative and find its maximum/minimum values
BC_SPCA
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Jun 21, 2022
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In the class on this, what solution method(s) did they teach? Use one of those. (I’m not being snarky, just saying the instructor expects to see it answered the way taught.)
chunichi_shonen
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Jun 21, 2022
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chunichi_shonen
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x^2 = positive smile of graph
-x^2 = negative/sad mouth of graph
+1 is where f(x) cuts through y-axis
ACristinaTLMD20
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Jun 21, 2022
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are u from Kurdistan ?
baileybram17
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Jun 21, 2022
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Or possibly through the use of a graphing calculator you could put the equation into "y=" and then it GRAPH and match the graph on the screen to the one on paper.
bgeurens
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Jun 21, 2022
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When x=0 f(x) = 1. Graph A fits.
mohammedsabeq
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Jun 21, 2022
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mohammedsabeq
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