How many times does the graph of 4x = 32 - x2 cross the x-axis ?
2 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
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