Solving Quadratic Equations

Front

What are the solutions of a quadratic equation called?

Back

The solutions, roots, x-intercepts, and zeros of a quadratic equation are all the same thing.

Front

How many zeros can a quadratic equation have?

Back

A quadratic equation can have 0, 1, or 2 zeros.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

How do you find the zeros of a quadratic equation?

Back

You can find the zeros by factoring the equation, using the quadratic formula, or completing the square.

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 roots of a quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if it's positive, there are 2 real roots; if zero, 1 real root; if negative, 2 complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the axis of symmetry in a parabola?

Back

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

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as a(x - r₁)(x - r₂), where r₁ and r₂ are the roots.

Front

How do you convert from factored form to standard form?

Back

To convert from factored form to standard form, expand the expression using the distributive property.