How many times does the graph of 4x = 32 - x2 cross the x-axis ?ОО
0 1
0 2
What are the solutions to the equation?
Answers
Answer:
Step-by-step explanation:
● 4x = 32 - x^2
Add x^2 to both sides
● 4x +x^2 = 32 -x^2+x^2
● x^2 +4x = 32
Substract 32 from both sides
● x^2+4x -32 =32-32
● x^2 +4x-32=0
That is a quadratic equation
We will use the determinant method
The determinant is b^2-4ac
● a = 1
● b = 4
● c = 32
● b^2-4ac = 4^2 -4×1×(-32) = 144
144 is positive so the parabola will cross the x-axis two times
● x = (-b -/+ √(b^2-4ac))/2a
● x = (-4 +/- 12) /2
● x = 8/2 or x= -16/2
● x = 4 or x =-8
The solutions are 4 and -8
Answer:
x=4 orx=- 8
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
4
x
=
−
x
2
+
32
Step 2: Subtract -x^2+32 from both sides.
4
x
−
(
−
x
2
+
32
)
=
−
x
2
+
32
−
(
−
x
2
+
32
)
x
2
+
4
x
−
32
=
0
Step 3: Factor left side of equation.
(
x
−
4
)
(
x
+
8
)
=
0
Step 4: Set factors equal to 0.
x
−
4
=
0
or
x
+
8
=
0
x
=
4
or
x
=
−
8
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Answers
= 8/49 x^-6/7 (1 - 6/x)
So the inflection point is at x = 6
hope it helps