Writing Quadratic Equations in Vertex & Standard Form

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

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

Front

What does the 'a' value in the vertex form indicate about the parabola?

Back

The 'a' value indicates the direction of the parabola: if 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you convert from vertex form to standard form?

Back

To convert from vertex form y = a(x - h)² + k to standard form, expand the squared term, distribute 'a', and combine like terms.

Front

What is the axis of symmetry in a quadratic equation?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = h.

Front

How can you determine if a parabola crosses the x-axis?

Back

A parabola crosses the x-axis if the quadratic equation has real solutions, which can be determined using the discriminant (b² - 4ac).

Front

What is the significance of the y-intercept in a quadratic equation?

Back

The y-intercept is the point where the graph of the quadratic equation crosses the y-axis, found by evaluating the equation at x = 0.

Front

What is the process to find the equation of a parabola given three points?

Back

To find the equation of a parabola given three points, you can use a graphing calculator's 'QuadReg' function after entering the points into a table.

Front

What does it mean for a parabola to have two x-intercepts?

Back

A parabola has two x-intercepts if it crosses the x-axis at two distinct points, indicating that the quadratic equation has two real and distinct solutions.