What is the significance of the value of $$b^2 - 4ac$$ in determining the nature of the roots?

The value of $$b^2 - 4ac$$ (the discriminant) determines the nature of the roots: positive means two distinct real roots, zero means one real root, and negative means two complex roots.

How do you simplify the expression $$\frac{2-4i}{1+3i}$$ ?

To simplify $$\frac{2-4i}{1+3i}$$ , multiply the numerator and denominator by the conjugate of the denominator: $$\frac{(2-4i)(1-3i)}{(1+3i)(1-3i)} = -1 - i$$ .

What is the vertex of a quadratic function?

The vertex of a quadratic function $$f(x) = ax^2 + bx + c$$ is the point where the graph changes direction. It can be found using the formula $$x = -\frac{b}{2a}$$ .

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

A quadratic function opens upwards if the coefficient $$a$$ (in $$ax^2 + bx + c$$ ) is positive, and it opens downwards if $$a$$ is negative.

What is the axis of symmetry for a quadratic function?

The axis of symmetry for a quadratic function $$f(x) = ax^2 + bx + c$$ is the vertical line given by $$x = -\frac{b}{2a}$$ .

What are the roots of a quadratic equation?

The roots of a quadratic equation are the values of $$x$$ that make the equation equal to zero. They can be found using the quadratic formula or by factoring.

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where $$a, b,$$ and $$c$$ are constants and $$a \neq 0$$ .

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 given by $$-\frac{b}{a}$$ and the product of the roots is given by $$\frac{c}{a}$$ .

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

The y-intercept of a quadratic function $$f(x) = ax^2 + bx + c$$ is found by evaluating $$f(0)$$ , which equals $$c$$ .

What is the importance of completing the square in solving quadratic equations?

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form $$(x - p)^2 = q$$ , making it easier to find the roots.

PreCalculus Quadratics Review Flashcard

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What does the discriminant tell us about the roots of a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

If the discriminant is zero, what can we say about the roots of the quadratic equation?

Back

If the discriminant is zero, the quadratic equation has exactly one real root, which is a repeated root.

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.CN.A.3

6.

FLASHCARD QUESTION

Front

What is a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

What does it mean for a quadratic equation to have no real solutions?

Back

Tags

CCSS.HSA-REI.B.4B

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