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 convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form, complete the square.

Front

What does the 'a' value in a quadratic equation indicate?

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 highest or lowest point of the parabola, depending on whether it opens upwards or 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 = h, where (h, k) is the vertex.

Front

How do you find the y-intercept of a quadratic equation?

Back

The y-intercept can be found by evaluating the equation at x = 0, which gives the point (0, c) in the standard form y = ax² + bx + c.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, found by solving the equation y = 0.

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 or x-intercepts of the quadratic.

Front

How do you determine if a quadratic function has a maximum or minimum value?

Back

If 'a' is positive, the function has a minimum value; if 'a' is negative, it has a maximum value.

Front

What is the relationship between the roots and the vertex of a parabola?

Back

The vertex lies on the axis of symmetry, which is equidistant from the roots of the parabola.