Graphing Quadratic Equations

Front

What is a quadratic equation?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is f(x) = ax² + bx + c.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the graph changes direction, representing the maximum or minimum value of the function.

Front

How do you find the vertex of a quadratic equation in standard form?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

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

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is f(x) = a(x - h)² + k, where (h, k) is the vertex.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert, complete the square on the quadratic expression.

Front

What are x-intercepts of a quadratic function?

Back

X-intercepts are the points where the graph of the function crosses the x-axis, found by solving f(x) = 0.

Front

How can you find the x-intercepts of a quadratic equation?

Back

You can find the x-intercepts by factoring the quadratic equation or using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

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.