Solve the quadratic equation by factoring: $$z^2 - 14z + 45 = 0$$

The solutions are $$z = 5$$ and $$z = 9$$ .

Solve the quadratic equation by factoring: $$m^2 - 100 = 0$$

The solutions are $$m = 10$$ and $$m = -10$$ .

Solve the equation using the zero product property: $$(x - 2)(3x + 1) = 0$$

The solutions are $$x = 2$$ and $$x = -\frac{1}{3}$$ .

What is the quadratic formula?

The quadratic formula is used to find the solutions of a quadratic equation and is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root, $$D = b^2 - 4ac$$ , which determines the nature of the roots.

What does it mean if the discriminant is positive?

If the discriminant is positive, the quadratic equation has two distinct real solutions.

What does it mean if the discriminant is zero?

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

What does it mean if the discriminant is negative?

If the discriminant is negative, the quadratic equation has no real solutions (the solutions are complex).

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.

What is the vertex of a parabola?

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

5.4 - 5,6: Solving Quadratics Flashcard 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 are the x-intercepts of a parabola?

Back

The x-intercepts of a parabola are the points where the graph intersects the x-axis, which correspond to the solutions of the quadratic equation.

3.

FLASHCARD QUESTION

Front

How can you determine the number of x-intercepts of a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

What is factoring in the context of quadratic equations?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the zero product property?

Back

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