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Which statement describes the effect on the parabola f(x)=2x²-5x+3 when it is changed to f (x)=2x2-5x+17
A. The parabola is translated up 1 unit.
B. The parabola is translated up 2 units.
C. The parabola is translated down 1 unit.
D. The parabola is translated down 2 units.
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D'Kayah Dominique Gipson, ID#*12 Growth: Math 6+ IN 2020 1.1
Question #4
9:19 AM
5/23/2024



Answer :

To determine the effect on the parabola when its equation changes from [tex]\( f(x) = 2x^2 - 5x + 3 \)[/tex] to [tex]\( f(x) = 2x^2 - 5x + 17 \)[/tex], let's analyze the difference between the two equations step by step.

1. Understanding the Components of a Parabola:

The general form of a quadratic equation is [tex]\( f(x) = ax^2 + bx + c \)[/tex], where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants. The [tex]\( c \)[/tex] term, also known as the constant term, affects the vertical position of the parabola but does not influence its shape or orientation.

2. Identifying Changes in the Equations:

- The initial equation is: [tex]\( f(x) = 2x^2 - 5x + 3 \)[/tex]
- The changed equation is: [tex]\( f(x) = 2x^2 - 5x + 17 \)[/tex]

By comparing these two equations, we can see that the coefficients of [tex]\( x^2 \)[/tex] and [tex]\( x \)[/tex] (i.e., [tex]\( 2 \)[/tex] and [tex]\( -5 \)[/tex]) remain unchanged. The only difference lies in the constant term:

- Initial constant term: 3
- Changed constant term: 17

3. Calculating the Vertical Shift:

To find out the vertical shift, we subtract the initial constant term from the changed constant term:

[tex]\( 17 - 3 = 14 \)[/tex]

This positive result indicates that the parabola is shifted upward.

4. Concluding the Shift:

The change from [tex]\( f(x) = 2x^2 - 5x + 3 \)[/tex] to [tex]\( f(x) = 2x^2 - 5x + 17 \)[/tex] results in the parabola being translated upward by 14 units.

However, let's review the answer choices given in the question:

A. The parabola is translated up 1 unit.
B. The parabola is translated up 2 units.
C. The parabola is translated down 1 unit.
D. The parabola is translated down 2 units.

None of these choices correctly match the actual shift of 14 units upward. Given the provided choices, none are correct for this specific problem unless there was a typographical error in the listing of options. The correct analysis shows an upward shift of 14 units.