Solving Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, using the quadratic formula, completing the square, and graphing.

Tags

CCSS.HSA-REI.B.4B

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x). Then, rewrite the equation in factored form.

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola is the highest or lowest point on the graph, found at the coordinates (h, k), where h = -b/(2a) and k is the value of the quadratic function at h.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

How do you complete the square for a quadratic equation?

Back

To complete the square, rearrange the equation to isolate the constant term, then add and subtract (b/2)² to form a perfect square trinomial.

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, representing the x-intercepts of the graph.

Tags

CCSS.HSF-IF.C.7A

Front

How do you round answers to the nearest hundredth?

Back

To round to the nearest hundredth, look at the third decimal place: if it's 5 or greater, round up the second decimal place by one; if it's less than 5, keep the second decimal place the same.

Tags

CCSS.5.NBT.A.4