Writing Quadratics Given Points/Solutions

Front

What is the vertex form of a quadratic function?

Back

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

Front

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

Back

To find the vertex of a quadratic function in standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

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 ax² + bx + c = 0.

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 is the x-coordinate of the vertex.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

Front

What are the roots of a quadratic function?

Back

The roots (or zeros) of a quadratic function are the values of x for which the function equals zero, representing the x-intercepts of the graph.

Front

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

Back

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

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 do you convert a quadratic function from standard form to vertex form?

Back

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

Front

What is the relationship between the vertex and the axis of symmetry?

Back

The vertex lies on the axis of symmetry, which is the line that divides the parabola into two equal halves.