Quadratic Formula

How many solutions does the following quadratic equation have: @@x^2-10x+25@@

• 0 Solutions (Discriminant is less than 0)

• 1 Solution (Discriminant is 0)

• 2 Solutions (Discriminant is greater than 0)

• Infinite Solutions (All values of x are solutions)

How many solutions does the following quadratic equation have: @@5x^2+9x-4@@?

• 0 Solutions (Discriminant is -1)

• 1 Solution (Discriminant is 0)

• 2 Solutions (Discriminant is 161)

• 3 Solutions (Discriminant is 5)

• x = -1, x = -4/5

• x = 1, x = 4/5

• x = -2, x = -3/5

• x = 0, x = -1/5

Identify the values of a, b, and c in the equation @@2x^2 - 3x - 5 = 0@@.

• a = 1, b = -3, c = -5

• a = 2, b = -3, c = -5

• a = 2, b = 3, c = 5

• a = 2, b = -3, c = 5

What is the Quadratic Formula?

• @@x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}@@

• @@x = \frac{{-b}}{{2a}}@@

• @@x = -b \pm \sqrt{c}@@

• @@x = \frac{{-b \pm \sqrt{{b^2 + 4ac}}}}{{2a}}@@

Solve the equation @@x^2 + 4x - 40 = -8@@ using the Quadratic Formula.

• x = -8 and x = 4

• x = -6 and x = 6

• x = -10 and x = 2

• x = -4 and x = 10

What does the discriminant of a quadratic equation tell us?

• It determines the number of solutions for the equation.

• It indicates the slope of the quadratic function.

• It tells us the maximum value of the quadratic function.

• It determines the nature of the roots of the quadratic equation.

What is a quadratic equation?

• A polynomial equation of degree 1

• A polynomial equation of degree 2, typically in the form @@ax^2 + bx + c = 0@@, where a, b, and c are constants and a ≠ 0.

• An equation that has no solutions

• A linear equation that graphs to a straight line.

How many solutions does the following quadratic equation have: @@11x^2+x+8@@

• 0 Solutions (Discriminant is -351)

• 1 Solution (Discriminant is 0)

• 2 Solutions (Discriminant is 25)

• Infinite Solutions (Discriminant is 0)

Solve the equation @@x^2 + 4x + 3 = 0@@ using the Quadratic Formula.

• x = -1 and x = -3

• x = 1 and x = 3

• x = -2 and x = -1

• x = 0 and x = -4