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

A quadratic opens upwards if the coefficient $$a > 0$$ and downwards if $$a

What is the maximum or minimum value of a quadratic function?

The maximum or minimum value of a quadratic function occurs at the vertex, which can be found using the vertex form or by substituting the axis of symmetry into the function.

Solve the quadratic equation: $$x^2 + 4x - 40 = -8$$

The solutions are $$x = -8$$ and $$x = 4$$ .

What is the relationship between the roots and 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 a perfect square trinomial?

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as $$(x + a)^2 = x^2 + 2ax + a^2$$ .

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

The vertex represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

How can you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, and intercepts, then plot these points and draw a smooth curve through them.

What is the effect of changing the value of 'a' in a quadratic equation?

Changing the value of 'a' affects the width and direction of the parabola: larger absolute values of 'a' make the parabola narrower, while smaller absolute values make it wider.

Quadratic Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

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