How do you solve the equation $$x^2 = -x + 1$$ ?

Rearranging gives $$x^2 + x - 1 = 0$$ . Use the Quadratic Formula: $$x = \frac{{-1 \pm \sqrt{{1^2 - 4(1)(-1)}}}}{{2(1)}} = \frac{{-1 \pm \sqrt{5}}}{2}$$ .

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

The discriminant determines the nature of the roots of the quadratic equation: it indicates whether the roots are real or complex and how many solutions exist.

How do you solve $$3x^2 - 21 = 3$$ using the Square Roots method?

First, simplify to $$3x^2 = 24$$ , then divide by 3 to get $$x^2 = 8$$ . Taking the square root gives $$x = \pm \sqrt{8} = \pm 2\sqrt{2}$$ .

What is the vertex form of a quadratic equation?

The vertex form of a quadratic equation is $$y = a(x - h)^2 + k$$ , 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, given by the formula $$x = -\frac{b}{2a}$$ .

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

The leading coefficient (the value of $$a$$ in $$ax^2 + bx + c$$ ) determines the direction of the parabola: if $$a > 0$$ , it opens upwards; if $$a

How can you verify your solutions to a quadratic equation?

You can verify solutions by substituting them back into the original equation to see if they satisfy the equation.

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 $$\frac{c}{a}$$ .

Flashcard over choosing the best method Flashcards

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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

When should you use the Square Root Method?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

What does it mean if a quadratic equation has 0 solutions?

Back

A quadratic equation has 0 solutions when the discriminant (the part under the square root in the Quadratic Formula) is less than 0, indicating that there are no real roots.

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What is the process of completing the square?

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of expressing a quadratic equation as a product of two binomials, allowing for easier solution of the equation.

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

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