QUIZIZZ Solving Quadratic Equations Quizs

Solve the quadratic equation: @@9x^2 - 7x - 4 = 0@@ using the quadratic formula.

• @@x = rac{10}{9}@@ and @@x = -rac{1}{3}@@

• @@x = rac{7 + 13}{18} = rac{10}{9}@@ and @@x = rac{7 - 13}{18} = rac{1}{3}@@

• @@x = rac{7 + 13}{18} = rac{10}{9}@@ and @@x = rac{7 - 13}{18} = rac{4}{9}@@

• @@x = rac{7 + 13}{18} = rac{10}{9}@@ and @@x = rac{7 - 13}{18} = -rac{2}{3}@@

What is the vertex form of a quadratic equation?

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

• y = a(x + h)^2 + k

• y = a(x - h)^2 - k

What is the axis of symmetry for a quadratic function?

• @@x = -\frac{b}{2a}@@

• @@x = \frac{b}{2a}@@

• @@x = -b@@

• @@x = 0@@

What is the standard form of a quadratic equation?

• @@ax^2 + bx + c = 0@@ where a, b, and c are constants and @@a \neq 0@@

• @@x^2 + y^2 = r^2@@

• @@y = mx + b@@

• @@ax^2 + bx + c = d@@ where a, b, and c are constants

Solve the quadratic equation: @@4x^2 - 9 = 0@@

• x = 2

• x = 0

• x = \frac{3}{2}

• x = -\frac{3}{2}

What does the discriminant tell you about a quadratic equation?

• The discriminant indicates the number of solutions to the equation.

• The discriminant tells you the slope of the quadratic function.

• The discriminant indicates the nature of the roots: if @@D > 0@@ there are two distinct real roots; if @@D = 0@@ there is one real root (a repeated root); if @@D < 0@@ there are no real roots.

• The discriminant shows the maximum value of the quadratic function.

How do you convert a quadratic equation from vertex form to standard form?

• Use the 'Tic-Tac-Toe' (Area Model) to expand the squared part, then distribute the value of 'a' and combine like terms to simplify completely, adding/subtracting the value of k to get the Standard Form.

• Simply rewrite the equation as @@y=ax^2+bx+c@@ without any further calculations.

• Substitute h and k directly into the standard form equation without any expansion.

• Factor the quadratic equation to find the roots and then write it in standard form.

What is the significance of the leading coefficient "a" in a quadratic equation?

• It determines the vertex of the parabola.

• It affects the width of the parabola.

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

• It indicates the maximum value of the quadratic function.

How do you complete the square for the equation @@x^2 - 4x = 20@@?

• Rewrite the equation as @@(x - 2)^2 = 24@@

• Rewrite the equation as @@(x + 2)^2 = 24@@

• Rewrite the equation as @@(x - 4)^2 = 20@@

• Rewrite the equation as @@(x + 4)^2 = 20@@