In which pair of numbers is the first number of the multiple of the second number?
1 answer:
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The option (D) the graph crosses the x-axis at the point (2, 0) is correct because the graph crosses x-axis at points (0, 0), (5, 0), (-2, 0), and (2, 0).
<h3>What is a function?</h3>It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The correct question is in the picture please refer to the attached picture.
We have a function:
f(x) = x⁴ - 5x³ - 4x² + 20x
By using factorization method:
By using zero product rule:
x = 0
x = 5
x = -2
x = 2
The graph crosses the x-axis at points (0, 0), (5, 0), (-2, 0), and (2, 0)
Thus, the option (D) the graph crosses the x-axis at the point (2, 0) is correct because the graph crosses the x-axis at points (0, 0), (5, 0), (-2, 0), and (2, 0).
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We know that
the equation of a vertical parabola in vertex form
y=a*(x-h)²+k
(h,k)------> (0,5)
y=a*(x-0)²+5
y=a*x²+5
substitute the point (2,9) in the equation
9=a*(2)²+5------> 9=4*a+5-------> 4*a=9-5-----> 4*a=4-----> a=1
the equation of the vertical parabola is
y=x²+5
the equation of a horizontal parabola in vertex form
x=a*(y-k)²+h
(h,k)------> (0,5)
x=a*(y-5)²+0
x=a*(y-5)²
substitute the point (2,9) in the equation
2=a*(9-5)²------> 2=16*a------> a=1/8
the equation of the horizontal parabola is
x=(1/8)*(y-5)²
the answer is
the equation of the vertical parabola is y=x²+5
the equation of the horizontal parabola is x=(1/8)*(y-5)²
see the attached figure
the equation of a vertical parabola in vertex form
y=a*(x-h)²+k
(h,k)------> (0,5)
y=a*(x-0)²+5
y=a*x²+5
substitute the point (2,9) in the equation
9=a*(2)²+5------> 9=4*a+5-------> 4*a=9-5-----> 4*a=4-----> a=1
the equation of the vertical parabola is
y=x²+5
the equation of a horizontal parabola in vertex form
x=a*(y-k)²+h
(h,k)------> (0,5)
x=a*(y-5)²+0
x=a*(y-5)²
substitute the point (2,9) in the equation
2=a*(9-5)²------> 2=16*a------> a=1/8
the equation of the horizontal parabola is
x=(1/8)*(y-5)²
the answer is
the equation of the vertical parabola is y=x²+5
the equation of the horizontal parabola is x=(1/8)*(y-5)²
see the attached figure