What is the first step in solving $$x^2 + 10x + 21 = 0$$ by completing the square?

The first step is to subtract 21 from both sides to isolate the quadratic expression: $$x^2 + 10x = -21$$ .

What is the zero product property?

The zero product property states that if $$ab = 0$$ , then either $$a = 0$$ or $$b = 0$$ . This is used to solve factored quadratic equations.

How do you determine the number of real solutions for a quadratic equation?

The number of real solutions can be determined using the discriminant $$D = b^2 - 4ac$$ . If $$D > 0$$ , there are two real solutions; if $$D = 0$$ , there is one real solution; if $$D

What is the vertex form of a quadratic equation?

The vertex form of a quadratic equation is given by $$y = a(x - h)^2 + k$$ , where $$(h, k)$$ is the vertex of the parabola.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves and is given by the formula $$x = -\frac{b}{2a}$$ .

How do you graph a quadratic function?

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

What is the significance of the leading coefficient in a quadratic equation?

The leading coefficient (the coefficient of $$x^2$$ ) determines the direction of the parabola: if it is positive, the parabola opens upwards; if negative, it opens downwards.

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 the purpose of the discriminant in the quadratic formula?

The discriminant helps determine the nature of the roots of the quadratic equation: real and distinct, real and equal, or complex.

All methods of solving quadratic equations Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

What does it mean to complete the square?

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What is factoring in the context of quadratic equations?

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

When can you use the square root method?

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What does the symbol ± represent in quadratic equations?

Back

The symbol ± indicates that there are two possible solutions, one for addition and one for subtraction, typically used after taking the square root.

Tags

CCSS.HSA-REI.B.4B

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