Introduction to the quadratic formula

Which value of b will cause the quadratic equation x2 + bx + 5 = 0 to have two real number solutions?

-5

What are the values of the coefficients and constant term of 0 = 4 - 7x2 + x in standard form?

-7, 1, 4

Which values of c will cause the quadratic equation -x2 + 3x + c = 0 to have no real number solutions? Check all that apply.

1, 2

Which equations have a leading coefficient of 3 and a constant term of -2? Check all that apply.

1,3,5

The discriminant of a quadratic equation is the value b2 - 4ac. What is the value of the discriminant of 0 = -2x2 + 6x + 13?

140

Consider the function f(x) = 3x2 + 7x + 2.

25, 2, two real number solutions

Which graph shows a quadratic function with a discriminant value of 0?

d.

Two of the steps in the derivation of the quadratic formula are shown below.

taking the square root of both sides of the equation

Describe how to derive the quadratic formula from a quadratic equation in standard form.

The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.