Vertex to 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

What is the shape of the graph of a quadratic function called?

Back

The U-shaped graph of a quadratic function is called a Parabola.

Front

What is the vertex of a quadratic function?

Back

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

Front

How do you identify the vertex from the vertex form of a quadratic equation?

Back

In vertex form, y = a(x - h)² + k, the vertex is the point (h, k).

Front

What does the 'a' in the standard form of a quadratic equation indicate?

Back

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

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 x = -b/(2a).

Front

What is the difference between standard form and vertex form of a quadratic equation?

Back

Standard form is y = ax² + bx + c, while vertex form is y = a(x - h)² + k, which makes it easier to identify the vertex.

Front

What is the intercept form of a quadratic equation?

Back

The intercept form is y = a(x - p)(x - q), where p and q are the x-intercepts of the parabola.

Front

How can you convert from vertex form to standard form?

Back

To convert, expand y = a(x - h)² + k to y = ax² - 2ahx + (ah² + k).

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: two real roots, one real root, or no real roots.