What is the equation of a line passes thru the point (4, 2) and is perpendicular to the line whose equation is y = ×/3 - 1 ??
2 answers:
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Answer:
They are represented by downward parabola
They have the same equations of line of symmetry
Their vertices have same x-coordinates but different y-coordinates
They have the same domains
They have different ranges
They have different maximum values at same x values
The graph of y = -2x² + 4 is the image of the graph y = -2x² after translation 4 units up
Step-by-step explanation:
y = -2x² is a quadratic equation which represents by a parabola
From the red graph:
The graph of y = -2x² is represented by downward parabola
It has a maximum vertex (0 , 0)
The line of symmetry at x = 0
Its maximum value = 0 at x = 0
Its domain is {x: x ∈ R}
Its range is {y: y ≤ 0}
From the blue graph:
The graph of y = -2x² + 4 is represented by down ward parabola
It has a maximum vertex (0 , 4)
The line of symmetry at x = 0
Its maximum value = 4 at x = 0
Its domain is {x: x ∈ R}
Its range is {y: y ≤ 4}
From the two graphs
They are represented by downward parabola
They have the same equations of line of symmetry
Their vertices have same x-coordinates but different y-coordinates
They have same domains
They have different ranges
They have different maximum values at same x values
The graph of y = -2x² + 4 is the image of the graph y = -2x² after translation 4 units up
The factored form of the equation 9x⁴y - 6x³y² + 3x²y³ is 3x²y(3x²-2xy+y²).
<h3>What is factored form?</h3>The product of a constant and two linear expressions in factored form. The roots of the function are the parameters and the x-intercepts of the graph. Often Factoring is referred to as the process of converting a quadratic function to factored form.
We need to write the given expression in the factored form, therefore, we will take the common terms out of the given expression,
1. Taking 3 as the common term, we will get,
2. Taking x² as the common term
3. Taking y as the common term,
Hence, the factored form of the equation 9x⁴y - 6x³y² + 3x²y³ is 3x²y(3x²-2xy+y²).
Learn more about Factored Form: