The equation below describes a parabola. If a is negative, which way does the parabola open? x = ay2
2 answers:
Answer:
The given parabola opens to the left.
Step-by-step explanation:
We are given,
The equation of the parabola is
If in the parabola,
<em>1. If 'a' is positive, then the parabola opens upwards or right.</em>
<em>2.</em><em> If 'a' is negative, then the parabola opens downwards or left.</em>
Moreover,
<em>3. If x is squared, then the parabola opens upwards or downwards.</em>
<em>4. </em><em>If y is squared, then the parabola opens left or right.</em>
Now, as we are given the parabola having and 'a' is negative.
Thus, from the points 4 and 2, we get,
The given parabola opens to the left.
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what numbers multliply to get -7 and add to get -6?
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the 2 integers can be 7 and 9 or -1 and 1 (both pairs of numbers work)
they are x and x+2
the product (x times (x+2)) is 1 less than 4 times their sum
x(x+2)=-1+4(x+x+2)
factor
what numbers multliply to get -7 and add to get -6?
-7 and 1
(x-7)(x+1)=0
set equal to 0
x-7=0
x=7
x+1=0
x=-1
so the x can be 7 or -1
the other number (x+2) can be 7 or 1
test each
7 and 9
7(9)=-1+4(7+9)
63=-1+4(16)
63=-1+64
63=63
true
-1 and 1
-1(1)=-1+4(-1+1)
-1=-1+4(0)
-1=-1+0
-1=-1
true
the 2 integers can be 7 and 9 or -1 and 1 (both pairs of numbers work)