Solve the equation $$x^2 + 3x - 9 = 0$$ using the Quadratic Formula.

Using the Quadratic Formula, the solutions are $$x = \frac{-3 \\pm \sqrt{15}}{2}$$ .

What is the vertex form of a quadratic function?

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

How can you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, and intercepts, then plot points and draw a smooth curve.

What does it mean if a quadratic function opens upwards?

If a quadratic function opens upwards, the coefficient 'a' in the standard form $$y = ax^2 + bx + c$$ is positive.

What does it mean if a quadratic function opens downwards?

If a quadratic function opens downwards, the coefficient 'a' in the standard form $$y = ax^2 + bx + c$$ is negative.

Solve the equation $$2x^2 - 5x + 3 = 0$$ using the Quadratic Formula.

Using the Quadratic Formula, the solutions are $$x = \frac{5 \\pm \sqrt{1}}{4}$$ .

What is the axis of symmetry for a quadratic function?

The axis of symmetry for a quadratic function is given by the formula $$x = -\frac{b}{2a}$$ .

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

The maximum or minimum value occurs at the vertex, and can be found by substituting the x-coordinate of the vertex into the function.

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

Quadratic Formula Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

2.

FLASHCARD QUESTION

Front

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

Back

3.

FLASHCARD QUESTION

Front

If the discriminant is equal to 0, how many real solutions are there?

Back

There is 1 real solution.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the first step in applying the Quadratic Formula?

Back

6.

FLASHCARD QUESTION

Front

How do you determine if a quadratic equation has real solutions?

Back

7.

FLASHCARD QUESTION

Front

What is the significance of the term 'quadratic'?

Back

The term 'quadratic' comes from 'quadratus', which means square in Latin, indicating that the highest degree of the variable in the equation is 2.

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