What is the value of the discriminant for the equation $$x^2 + 4x - 40 = 0$$ ?

The discriminant is calculated as $$b^2 - 4ac = 4^2 - 4(1)(-40) = 16 + 160 = 176$$ , which is positive, indicating 2 real solutions.

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

Using the quadratic formula, the solutions are $$x = -\frac{1}{3}, x = -5$$ .

How do you determine the number of solutions from the discriminant?

You can determine the number of solutions by evaluating the discriminant: If $$b^2 - 4ac > 0$$ , there are 2 solutions; if $$b^2 - 4ac = 0$$ , there is 1 solution; if $$b^2 - 4ac

What does it mean if a quadratic graph touches the x-axis at one point?

If a quadratic graph touches the x-axis at one point, it means the discriminant is zero, indicating there is exactly one real solution.

What is the vertex of a parabola represented by a quadratic equation?

The vertex of a parabola represented by the quadratic equation $$y = ax^2 + bx + c$$ can be found using the formula $$x = -\frac{b}{2a}$$ .

How can you find the axis of symmetry for a quadratic function?

The axis of symmetry for a quadratic function $$y = ax^2 + bx + c$$ is given by the line $$x = -\frac{b}{2a}$$ .

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

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

What is the graphical representation of a quadratic function?

The graphical representation of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient $$a$$ .

How do you solve a quadratic equation by factoring?

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

What is the role of the leading coefficient in a quadratic equation?

The leading coefficient (the coefficient of $$x^2$$ ) determines the direction of the parabola: if it is positive, the parabola opens upwards; if negative, it opens downwards.

Quadratic Formula and Discriminant Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What does the discriminant tell us about a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

If the discriminant is equal to 0, how many solutions does the quadratic equation have?

Back

If the discriminant is equal to 0, the quadratic equation has exactly 1 real solution.

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What is the significance of a negative discriminant?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

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