Determine the nature of the solutions of a quadratic using the quadratic formula

Determine the nature of the solutions of a quadratic using the quadratic formula

In this lesson you will learn how to determine if a quadratic function has two real roots, one real root, or no real roots by looking at the discriminant.

ADDITIONAL MATERIALS

STANDARDS

CCSS.HSA-REI.B.4.b Solve quadratic equations by inspection (e.g., for 𝘹² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝘢 ± 𝘣𝘪 for real numbers 𝘢 and 𝘣.

TEKS.A2.4.F solve quadratic and square root equations;

TEKS.A1.6.C write quadratic functions when given real solutions and graphs of their related equations.

TEKS.A1.8.A solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula; and

TEKS.A1.12.E solve mathematic and scientific formulas, and other literal equations, for a specified variable.

IN.AI.QE.5 Represent real-world problems using quadratic equations in one or two variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable.

IN.AI.QE.4 Solve quadratic equations in one variable by inspection (e.g., for x^2 = 49), finding square roots, using the quadratic formula, and factoring, as appropriate to the initial form of the equation.

VA.EI.A.4.e practical problems involving equations and systems of equations.

VA.F.A.7.c zeros;

VA.EI.AII.3.b quadratic equations over the set of complex numbers;

VA.EI.A.4.b quadratic equations in one variable algebraically;