How do you solve a quadratic equation by factoring?

To solve by factoring, express the quadratic in the form $$(px + q)(rx + s) = 0$$ and set each factor to zero to find the values of x.

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

The coefficient 'a' determines the direction of the parabola (upward or downward), 'b' affects the position of the vertex, and 'c' represents the y-intercept.

How can you determine the number of real solutions to a quadratic equation?

By calculating the discriminant $$D = b^2 - 4ac$$ ; the sign of D indicates the number of real solutions.

What is the vertex form of a quadratic equation?

The vertex form is given by $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

How do you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, intercepts, and plot points to sketch the parabola.

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

How do you apply the quadratic formula to solve an equation?

Substitute the values of a, b, and c from the quadratic equation into the quadratic formula $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ and simplify.

What is the role of the initial velocity in projectile motion modeled by quadratic equations?

The initial velocity affects the height and time of flight of the projectile, influencing the coefficients in the quadratic equation that models its motion.

Solving 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 is the quadratic formula?

Back

4.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation tell us?

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

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

Back

The maximum or minimum value occurs at the vertex of the parabola. If a > 0, the parabola opens upwards and has a minimum; if a < 0, it opens downwards and has a maximum.

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