What is the axis of symmetry for the quadratic equation $$y=4x^2-8x+9$$ ?

The axis of symmetry is given by the formula $$x=-\frac{b}{2a}$$ . For this equation, it is $$x=1$$ .

What does the discriminant of a quadratic equation tell you?

The discriminant $$D=b^2-4ac$$ indicates the nature of the roots: if D>0, two real roots; D=0, one real root; D

What is the standard form of a quadratic function?

The standard form is $$f(x)=ax^2+bx+c$$ .

How do you identify a quadratic function from a set of data points?

Look for a pattern where the second differences of the y-values are constant.

What is the significance of the vertex in a quadratic function?

The vertex represents the maximum or minimum point of the parabola.

What is the formula for the axis of symmetry of a parabola?

The axis of symmetry is given by $$x=-\frac{b}{2a}$$ .

What is the effect of changing the value of 'a' in the quadratic function $$f(x)=ax^2+bx+c$$ ?

Changing 'a' affects the width and direction of the parabola: if |a|>1, the parabola is narrower; if |a|

What is the range of the function $$y=-3x^2-7x+8$$ ?

The range is $$(-\infty, k)$$ where k is the maximum value of the function.

How do you determine if a quadratic function opens upwards or downwards?

If the leading coefficient 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

Unit 4B Review 2024 Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

Back

2.

FLASHCARD QUESTION

Front

Which equation represents a downward-opening parabola with vertex at (4, -1)?

Back

3.

FLASHCARD QUESTION

Front

What type of function is represented by a table of values that shows a constant second difference?

Back

The function is quadratic.

4.

FLASHCARD QUESTION

Front

How do you determine the range of a quadratic function that opens downwards?

Back

5.

FLASHCARD QUESTION

Front

What direction does the parabola open if the leading coefficient is negative?

Back

The parabola opens down.

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