Solve the equation using the quadratic formula: $$2m^2 + 2m - 12 = 0$$

The solutions are $$m = 2, m = -3$$ .

Solve the equation using the quadratic formula: $$2x^2 - 9x - 35 = 0$$

The solutions are $$x = -5/2, x = 7$$ .

Solve the equation using the quadratic formula: $$3x^2 + 16x + 5 = 0$$

The solutions are $$x = -\frac{1}{3}, x = -5$$ .

What is the vertex form of a quadratic equation?

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

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 axis of symmetry in a quadratic function?

The axis of symmetry of a quadratic function is the vertical line that divides the parabola into two mirror-image halves, given by the formula $$x = -\frac{b}{2a}$$ .

What does it mean if the discriminant is zero?

If the discriminant is zero, the quadratic equation has exactly one real root, meaning the parabola touches the x-axis at one point (the vertex).

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

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

How can you determine the number of real solutions from the discriminant?

You can determine the number of real solutions by evaluating the discriminant: if it is positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

What is the relationship between the roots and the coefficients of a quadratic equation?

The sum of the roots (solutions) of the quadratic equation $$ax^2 + bx + c = 0$$ is given by $$-b/a$$ , and the product of the roots is given by $$c/a$$ .

Quadratic formula Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

2.

FLASHCARD QUESTION

Front

What does the discriminant represent in a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

How do you solve a quadratic equation using the quadratic formula?

Back

4.

FLASHCARD QUESTION

Front

Why do we set quadratic equations equal to zero?

Back

Quadratic equations are set equal to zero to find the x-intercepts of the graph, which occur where the value of y is zero.

5.

FLASHCARD QUESTION

Front

What are the x-intercepts of a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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