Algebra: Quadratic Equations flashcards

Question 1

What is the general form of a quadratic equation?

Accepted Answer

ax^2 + bx + c = 0, with a ≠ 0

Question 2

What is the name of the curve that graphs y = ax^2 + bx + c?

Accepted Answer

A parabola

Question 3

What is the quadratic formula for ax^2 + bx + c = 0 (a ≠ 0)?

Accepted Answer

x = (−b ± √(b^2 − 4ac)) / (2a)

Question 4

In the quadratic formula, what is the expression b^2 − 4ac called?

Accepted Answer

The discriminant

Question 5

If b^2 − 4ac > 0, how many solutions does ax^2 + bx + c = 0 have?

Accepted Answer

Two solutions

Question 6

If b^2 − 4ac = 0, how many solutions does ax^2 + bx + c = 0 have?

Accepted Answer

One solution

Question 7

If b^2 − 4ac < 0, how many real solutions does ax^2 + bx + c = 0 have?

Accepted Answer

None (no real solutions)

Question 8

What does the Square Root Property say about x^2 = k when k ≥ 0?

Accepted Answer

x = √k or x = −√k

Question 9

What is (a + b)^2 expanded, for real a and b?

Accepted Answer

a^2 + 2ab + b^2

Question 10

What number completes the square of x^2 + bx?

Accepted Answer

(b/2)^2, that is, half of b, squared

Question 11

What is completing the square used for in algebra?

Accepted Answer

It is a method of solving quadratic equations

Question 12

For y = ax^2 + bx + c, what is the equation of the axis of symmetry?

Accepted Answer

x = −b/(2a)

Question 13

What kind of line is the axis of symmetry of the parabola y = ax^2 + bx + c?

Accepted Answer

A vertical line through the middle of the parabola

Question 14

What is the vertex of a parabola?

Accepted Answer

The point of the parabola on its axis of symmetry; its highest or lowest point

Question 15

For y = ax^2 + bx + c, what is the x-coordinate of the vertex?

Accepted Answer

−b/(2a)

Question 16

For y = ax^2 + bx + c, which way does the parabola open if a > 0?

Accepted Answer

Upward

Question 17

For y = ax^2 + bx + c, which way does the parabola open if a < 0?

Accepted Answer

Downward

Question 18

At the x-intercepts of a parabola, what is the value of y?

Accepted Answer

y = 0

Question 19

At the y-intercept of a parabola, what is the value of x?

Accepted Answer

x = 0

Question 20

If a parabola opens upward, what does the y-coordinate of its vertex give?

Accepted Answer

The minimum value of the quadratic

Question 21

If a parabola opens downward, what does the y-coordinate of its vertex give?

Accepted Answer

The maximum value of the quadratic

Question 22

In a right triangle with legs a and b and hypotenuse c, what does the Pythagorean theorem state?

Accepted Answer

a^2 + b^2 = c^2

Question 23

What is the area of a triangle with base b and height h?

Accepted Answer

A = (1/2)bh

Algebra: Quadratic Equations flashcards

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