How do you solve the equation $$x^2 - 10x + 25 = 49$$ by factoring?

First, rewrite it as $$(x - 5)^2 = 49$$ . Then take the square root of both sides to get $$x - 5 = 7$$ or $$x - 5 = -7$$ , leading to solutions $$x = 12$$ and $$x = -2$$ .

What is the factored form of $$x^2 - 9x + 20$$ ?

The factored form is $$(x - 4)(x - 5)$$ , and the solutions are $$x = 4$$ and $$x = 5$$ .

What is the solution to the equation $$x^2 - 6x + 9 = 0$$ ?

The factored form is $$(x - 3)(x - 3)$$ , which gives the solution $$x = 3$$ .

What is the significance of the roots of a quadratic equation?

The roots of a quadratic equation represent the x-intercepts of the parabola on a graph, indicating where the graph intersects the x-axis.

What does it mean for a quadratic equation to be not factorable?

A quadratic equation is not factorable over the real numbers if its discriminant is less than zero, meaning it has no real roots.

How do you convert a quadratic equation to vertex form?

To convert to vertex form, use the method of completing the square to rewrite the equation as $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex.

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 equation $$x = -\frac{b}{2a}$$ .

How can you verify the solutions of a quadratic equation?

You can verify the solutions by substituting them back into the original equation to check if both sides are equal.

What is the relationship between the coefficients and the roots 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 $$\frac{c}{a}$$ .

Solving Quadratic Equations Review Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to factor a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What is the process of completing the square?

Back

4.

FLASHCARD QUESTION

Front

How do you find the vertex of a parabola represented by a quadratic equation?

Back

5.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

6.

FLASHCARD QUESTION

Front

What is the discriminant in a quadratic equation?

Back

7.

FLASHCARD QUESTION

Front

Back

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