The line plot below shows how many points Trevor scored in 20 games.
1 answer:
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The expression is 
1. We start by factorizing the equation
:
The roots of f(x) occur at the x-values that result in f(x) being equal to 0.
From the factorized representation of the function, we find that the roots are:
-3 with a multiplicity of 1,
3 with a multiplicity of 1,
0 with a multiplicity of 3
(the multiplicity indicates the exponent of each factor in the function f(x)).
2.
The behavior of f(x) at both ends aligns with that of
, known for its specific graphical shape. Refer to the attached image.
(similarly, the end behavior of a polynomial of even degree could be likened to the end behavior of
)
Thus, like the graph of, the graph of behaves as follows:
"As x approaches negative infinity, f(x) approaches negative infinity, and as x approaches positive infinity, f(x) approaches positive infinity. "
1. We start by factorizing the equation
The roots of f(x) occur at the x-values that result in f(x) being equal to 0.
From the factorized representation of the function, we find that the roots are:
-3 with a multiplicity of 1,
3 with a multiplicity of 1,
0 with a multiplicity of 3
(the multiplicity indicates the exponent of each factor in the function f(x)).
2.
The behavior of f(x) at both ends aligns with that of
(similarly, the end behavior of a polynomial of even degree could be likened to the end behavior of
Thus, like the graph of
"As x approaches negative infinity, f(x) approaches negative infinity, and as x approaches positive infinity, f(x) approaches positive infinity. "
Response: The solution is f(x) = (x-3)²-h = (x-3-√h)(x-3+√h).
Detailed explanation: We are tasked with writing a quadratic equation in factored format that has a vertex at an x-coordinate of 3 and two separate roots.
A quadratic function with a vertex at x-coordinate k is represented in the form of a parabola:
In this case, both 'k' and 'h' are real numbers.
Given that the vertex's x-coordinate is 3, we have k = 3.
Consequently, the quadratic function can be expressed as
This represents the required factored form for the quadratic equation.
Refer to the included graph where the vertex has an x-coordinate of 3, and h is assumed to be 2 units.
