Graphing Quadratics in Standard Form

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the equation to find y.

Front

What is the significance of the vertex in a quadratic graph?

Back

The vertex represents the maximum or minimum point of the graph, depending on the direction of the parabola.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' in the standard form y = ax² + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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 does it mean for a quadratic function to have a minimum or maximum?

Back

A quadratic function has a minimum if it opens upwards (a > 0) and a maximum if it opens downwards (a < 0).

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, find the vertex, y-intercept, and additional points, then plot these points and draw a smooth curve.

Front

What is the formula for finding the y-coordinate of the vertex?

Back

The y-coordinate of the vertex can be found by substituting x = -b/(2a) into the quadratic equation.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots (or x-intercepts) are the points where the graph intersects the x-axis, and they can be found using the quadratic formula.