What does the term 'parent function' refer to in quadratic transformations?

The parent function for quadratics is $$y = x^2$$ . It serves as the basic form from which other quadratic functions are derived through transformations.

What is the effect of a negative coefficient in front of a quadratic function?

A negative coefficient reflects the graph of the quadratic function across the x-axis, changing the direction of the parabola.

How do you determine the direction of a parabola?

The direction of a parabola is determined by the sign of the coefficient $$a$$ in the quadratic function $$y = ax^2 + bx + c$$ . If $$a > 0$$ , the parabola opens upwards; if $$a

What is the significance of the constant term in a quadratic function?

The constant term $$c$$ in the quadratic function $$y = ax^2 + bx + c$$ represents the y-intercept, which is the point where the graph intersects the y-axis.

What is the transformation represented by $$y = (x - 3)^2 + 2$$ ?

This transformation represents a horizontal translation 3 units to the right and a vertical translation 2 units up from the parent function $$y = x^2$$ .

How do you identify a vertical stretch or shrink from a quadratic equation?

To identify a vertical stretch or shrink, look at the coefficient $$a$$ in the equation $$y = ax^2$$ . If $$|a| > 1$$ , it is a vertical stretch; if $$0

What is the effect of adding a constant to a quadratic function?

Adding a constant to a quadratic function shifts the graph vertically. For example, in $$y = x^2 + k$$ , the graph shifts up by $$k$$ units if $$k > 0$$ and down if $$k

How do you find the equation of a transformed quadratic function?

To find the equation of a transformed quadratic function, identify the transformations applied to the parent function $$y = x^2$$ and apply them in the form $$y = a(x - h)^2 + k$$ , where $$h$$ and $$k$$ represent horizontal and vertical shifts, respectively.

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Math

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Quadratic Transformations Review

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Mathematics

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9th - 12th Grade

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Practice Problem

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Hard

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CCSS

HSF-IF.C.7A

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FLASHCARD QUESTION

Front

What is a quadratic function?

Back

FLASHCARD QUESTION

Front

What does it mean to translate a graph vertically?

Back

Translating a graph vertically means shifting the entire graph up or down along the y-axis. For example, adding a constant to the function shifts it up, while subtracting a constant shifts it down.

FLASHCARD QUESTION

Front

What is a vertical stretch in a quadratic function?

Back

FLASHCARD QUESTION

Front

What is a vertical shrink in a quadratic function?

Back

FLASHCARD QUESTION

Front

How does a horizontal translation affect a quadratic function?

Back

FLASHCARD QUESTION

Front

What is the vertex of a quadratic function?

Back

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

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