Graphing Quadratics - Standard Form

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two mirror-image halves.

Front

What shape does the graph of a quadratic function take?

Back

The graph of a quadratic function is called a parabola.

Front

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

Back

For a quadratic in the form y = ax^2 + bx + c, 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 standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic function indicate about the parabola?

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

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

Back

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

Front

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

Back

If the coefficient 'a' in the quadratic function y = ax^2 + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the formula to find the y-coordinate of the vertex?

Back

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

Front

What is the role of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What does it mean for a quadratic function to have real roots?

Back

Real roots indicate the x-values where the graph of the quadratic intersects the x-axis.