What is the quadratic formula?

The quadratic formula is $$x = \frac{-b \textpm \textsqrt{b^2 - 4ac}}{2a}$$ , used to find the roots of a quadratic equation.

What does the discriminant tell us about the roots of a quadratic equation?

The discriminant, given by $$b^2 - 4ac$$ , indicates the nature of the roots: if positive, there are 2 real roots; if zero, there is 1 real root; if negative, there are no real roots.

How do you find the y-intercept of a quadratic equation?

The y-intercept can be found by evaluating the equation at $$x = 0$$ , which gives $$y = c$$ in the standard form $$y = ax^2 + bx + c$$ .

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

The coefficient 'a' determines the direction of the parabola: if $$a > 0$$ , it opens upwards; if $$a

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 vertex and roots.

How can you solve a quadratic equation by graphing?

To solve by graphing, plot the quadratic function and identify the points where the graph intersects the x-axis, which represent the roots.

What is a parabola's minimum or maximum value?

The minimum or maximum value of a parabola occurs at the vertex and is the y-coordinate of the vertex.

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

College Algebra Quadratic Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What does the graph of a quadratic equation look like?

Back

4.

FLASHCARD QUESTION

Front

What is the vertex of a parabola?

Back

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

5.

FLASHCARD QUESTION

Front

How do you find the vertex of a parabola in standard form?

Back

6.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a parabola?

Back

7.

FLASHCARD QUESTION

Front

What are the roots of a quadratic equation?

Back

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