How do you solve the equation $$x^2 + 4x - 40 = -8$$ using the Quadratic Formula?

First, rewrite it as $$x^2 + 4x + 32 = 0$$ . Then apply the Quadratic Formula to find the solutions.

What is the first step in solving the equation $$x^2 + 6x - 13 = 3$$ ?

Make it equal 0 by subtracting 3 from both sides, resulting in $$x^2 + 6x - 16 = 0$$ .

What are the roots of the equation $$k^2 - 12k + 23 = 0$$ ?

The roots are $$6 + \sqrt{13}$$ and $$6 - \sqrt{13}$$ .

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 does the discriminant of a quadratic equation tell us?

The discriminant, given by $$b^2 - 4ac$$ , indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

What is the process of completing the square?

Completing the square involves rewriting a quadratic equation in the form $$(x - p)^2 = q$$ to easily find the roots.

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

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, it opens upwards; if negative, it opens downwards.

How can you determine if a quadratic equation can be factored easily?

If the equation can be expressed as $$(x - p)(x - q) = 0$$ , where p and q are rational numbers, it can be factored easily.

What is the axis of symmetry in a quadratic function?

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

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

The maximum or minimum value occurs at the vertex, and can be found using the vertex form or by evaluating the function at the vertex coordinates.

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

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

Solving Quadratic Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

3.

FLASHCARD QUESTION

Front

What does it mean to solve a quadratic equation by factoring?

Back

4.

FLASHCARD QUESTION

Front

What must be true for an equation to be solved by factoring?

Back

The equation must be set equal to 0.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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