Standard and Vertex Forms and Graphs of Quadratic Functions

Front

What is the vertex of a parabola in standard form?

Back

The vertex of a parabola in standard form, y = ax^2 + bx + c, can be found using the formula: (h, k) where h = -b/(2a) and k = f(h).

Front

What is the axis of symmetry for a quadratic function in standard form?

Back

The axis of symmetry for a quadratic function in standard form, y = ax^2 + bx + c, is given by the line x = -b/(2a).

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form (y = ax^2 + bx + c) to vertex form (y = a(x-h)^2 + k), complete the square.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How can you identify the direction of a parabola from its equation?

Back

The direction of a parabola opens upwards if a > 0 and downwards if a < 0 in the equation y = ax^2 + bx + c.

Front

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

Back

The 'a' value in the vertex form y = a(x-h)^2 + k indicates the width and direction of the parabola. A larger |a| makes the parabola narrower.

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 find the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x^2.

Front

What is the effect of changing the 'h' value in vertex form?

Back

Changing the 'h' value in vertex form y = a(x-h)^2 + k shifts the graph horizontally. If h is positive, the graph shifts to the right; if negative, to the left.