What is the axis of symmetry for the quadratic function $$y = ax^2 + bx + c$$ ?

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

What is completing the square?

Completing the square is a method used to convert a quadratic equation into vertex form by adding and subtracting the square of half the coefficient of $$x$$ .

What is the quadratic formula?

The quadratic formula is used to find the roots of a quadratic equation and is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What does it mean for a quadratic function to have a maximum or minimum value?

A quadratic function has a maximum value if it opens downwards (a 0).

What is the factored form of a quadratic function?

The factored form of a quadratic function is written as $$y = a(x - r_1)(x - r_2)$$ , where $$r_1$$ and $$r_2$$ are the roots of the equation.

How do you find the y-intercept of a quadratic function?

The y-intercept of a quadratic function can be found by evaluating the function at $$x = 0$$ , which gives $$y = c$$ in the standard form $$y = ax^2 + bx + c$$ .

What is the relationship between the roots and the coefficients of a quadratic equation?

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

What is the role of the coefficient 'a' in a quadratic function?

The coefficient 'a' determines the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower, while a smaller absolute value makes it wider.

All Forms of Quadratics Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic function?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic function?

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

Back

The vertex of the function is (-3, 4).

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the significance of the discriminant in a quadratic equation?

Back

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