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Question 1

What is the standard form of a quadratic equation?

Answer 1

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Question 2

True or False: The graph of a quadratic function is a straight line.

Answer 2

False

Question 3

Fill in the blank: The highest power of x in a quadratic equation is ____.

Answer 3

2

Question 4

What does the ‘a’ value in a quadratic equation determine?

Answer 4

It determines the direction and width of the parabola.

Question 5

Which formula is used to find the roots of a quadratic equation?

Answer 5

The quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Question 6

What is the vertex of a parabola?

Answer 6

The vertex is the highest or lowest point of the parabola.

Question 7

True or False: A quadratic function can have at most two real roots.

Answer 7

True

Question 8

What is the axis of symmetry for a quadratic equation in standard form?

Answer 8

x = -b / (2a)

Question 9

What is the discriminant in a quadratic equation?

Answer 9

The discriminant is b² - 4ac and determines the nature of the roots.

Question 10

Fill in the blank: If the discriminant is positive, the quadratic has ____ real roots.

Answer 10

two

Question 11

What is the general shape of a quadratic function’s graph?

Answer 11

A parabola

Question 12

Choose the correct answer: The y-intercept of a quadratic equation ax² + bx + c is:

Answer 12

c

Question 13

What are the coordinates of the vertex for the quadratic equation y = a(x - h)² + k?

Answer 13

(h, k)

Question 14

True or False: Quadratic equations can be solved by factoring.

Answer 14

True

Question 15

What is the vertex form of a quadratic equation?

Answer 15

y = a(x - h)² + k

Question 16

Fill in the blank: The value of ‘a’ in the vertex form affects the ____ of the parabola.

Answer 16

direction and width

Question 17

What does it mean if a quadratic equation has complex roots?

Answer 17

It means the discriminant is negative and the roots are not real numbers.

Question 18

Choose the correct answer: The sum of the roots of the quadratic equation ax² + bx + c = 0 is:

Answer 18

-b/a

Question 19

What term describes the solutions to a quadratic equation?

Answer 19

Roots or zeros

Question 20

True or False: The parabola opens upwards if ‘a’ is positive.

Answer 20

True

Question 21

What is the formula for the axis of symmetry in a quadratic equation?

Answer 21

x = -b / (2a)

Question 22

Fill in the blank: A quadratic function can be represented in ____ form, vertex form, and factored form.

Answer 22

standard

Question 23

What does the term ‘factoring’ refer to in relation to quadratics?

Answer 23

Expressing the quadratic as a product of its linear factors.

Question 24

What is the factored form of a quadratic equation?

Answer 24

y = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots.

Question 25

True or False: The maximum or minimum value of a quadratic function occurs at the vertex.

Answer 25

True