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.

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.

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.

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.