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

$$0$$ (The discriminant is zero, indicating one real solution.)

For the quadratic equation $$3x^2 + 6x + 2 = 0$$ , what is the discriminant?

$$6$$ (The discriminant is positive, indicating two real solutions.)

What does a negative discriminant indicate about a quadratic equation?

It indicates that there are no real solutions.

How do you calculate the roots of a quadratic equation using the quadratic formula?

Substitute a, b, and c into $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What is the significance of the coefficients a, b, and c in a quadratic equation?

They determine the shape and position of the parabola represented by the equation.

What is the vertex of a parabola given by the quadratic equation $$y = ax^2 + bx + c$$ ?

The vertex can be found at $$x = -\frac{b}{2a}$$ .

How can you determine if a quadratic function opens upwards or downwards?

If a > 0, it opens upwards; if a

What is the axis of symmetry for the quadratic equation $$y = ax^2 + bx + c$$ ?

The axis of symmetry is given by $$x = -\frac{b}{2a}$$ .

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

The roots are the x-intercepts of the graph of the quadratic function.

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

The y-intercept is found by evaluating the equation at x = 0, which gives $$c$$ .

Quadratic formula and discriminant Flashcards

Student preview

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 the solutions of a quadratic equation?

Back

The discriminant determines the number of real solutions: if > 0, two solutions; if = 0, one solution; if < 0, no real solutions.

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

What is the formula for the discriminant of a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

Back

a = 2, b = -3, c = -5

5.

FLASHCARD QUESTION

Front

If the discriminant of a quadratic equation is equal to 4, how many real solutions are there?

Back

Two real solutions.

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

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