Graphing Quadratic Equations

Front

What is a quadratic equation?

Back

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

Front

What does the graph of a quadratic equation look like?

Back

The graph of a quadratic equation is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens downwards or upwards.

Front

What is the axis of symmetry in a quadratic graph?

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 are the zeros (or roots) of a quadratic equation?

Back

The zeros of a quadratic equation are the x-values where the graph intersects the x-axis, found by solving the equation ax² + bx + c = 0.

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, calculated using the vertex formula y = f(-b/(2a)).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What is the factored form of a quadratic equation?

Back

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

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

How do you graph a quadratic equation?

Back

To graph a quadratic equation, find the vertex, axis of symmetry, zeros, and plot additional points to shape the parabola.