What is the standard form of a quadratic equation?

The standard form is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants.

What does it mean if the discriminant is zero?

It means that the quadratic equation has exactly one real solution (a repeated root).

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

If the coefficient a (from $$ax^2 + bx + c$$ ) is positive, the parabola opens upwards; if a is negative, it opens downwards.

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

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ , and the corresponding y-value can be found by substituting x back into the equation.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is the vertical line that passes through the vertex, given by the equation $$x = -\frac{b}{2a}$$ .

What is the significance of the roots of a quadratic equation?

The roots are the x-values where the graph of the quadratic function intersects the x-axis.

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

The y-intercept can be found by evaluating the equation at x = 0, which gives $$c$$ in the standard form $$ax^2 + bx + c$$ .

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

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

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

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

If the discriminant is equal to -2, how many real solutions are there?

Back

None.

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What are the solutions of a quadratic equation also called?

Back

Roots, x-intercepts, or zeros.

5.

FLASHCARD QUESTION

Front

Back

76.

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

Back

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

7.

FLASHCARD QUESTION

Front

Back

x = -0.67, x = 6.

Tags

CCSS.HSA-REI.B.4B

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