Quadratic Formula

What is the significance of the coefficient 'a' in a quadratic equation?

• It determines the width of the parabola.

• It determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

• It affects the position of the vertex of the parabola.

• It indicates the number of real roots of the equation.

What is the axis of symmetry in a quadratic function?

• @@x = -\frac{b}{2a}@@

• @@y = -\frac{b}{2a}@@

• @@x = \frac{b}{2a}@@

• @@y = \frac{b}{2a}@@

Solve using the quadratic formula: @@2x^2 - 4x + 2 = 0@@

• x = 1

• x = 2

• x = 0

• x = -1

Solve using the quadratic formula: @@x^2 - 6x + 9 = 0@@

• x = 2

• x = 3

• x = 4

• x = 5

What is the standard form of a quadratic equation?

• @@ax^2 + bx + c = 0@@

• @@x^2 + y^2 = 1@@

• @@y = mx + b@@

• @@ax^2 + bx = 0@@

Solve using the quadratic formula: @@x^2 + 2x + 1 = 0@@

• x = 0

• x = -2

• x = -1

• x = 1

Solve using the quadratic formula: @@x^2 + 4x + 4 = 0@@

• x = -2

• x = 0

• x = 2

• x = -4

Solve using the quadratic formula: @@x^2 - 5x + 6 = 0@@

• x = 1 and x = 6

• x = 2 and x = 3

• x = -2 and x = -3

• x = 0 and x = 5

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

• The sum of the roots is @@-rac{b}{a}@@ and the product of the roots is @@rac{c}{a}@@.

• The sum of the roots is @@rac{b}{a}@@ and the product of the roots is @@-rac{c}{a}@@.

• The sum of the roots is @@0@@ and the product of the roots is @@1@@.

• The sum of the roots is @@rac{c}{b}@@ and the product of the roots is @@-rac{a}{b}@@.

• x = -2

• x = -3

• x = 0

• x = 2