Standard Form to Vertex 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

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 (y = a(x - h)² + k), you can complete the square.

Front

What is vertex form of a quadratic equation?

Back

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

Front

What does the vertex of a parabola represent?

Back

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

Front

Convert the equation y = x² + 4x + 11 into vertex form.

Back

y = (x + 2)² + 7

Front

Convert the equation y = x² - 6x + 10 into vertex form.

Back

y = (x - 3)² + 1

Front

Which of the following is a characteristic of a quadratic function?

Back

A quadratic function has a parabolic graph that can open 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 x = h in vertex form.

Front

Convert the equation x² - 12x + 40 into vertex form.

Back

(x - 6)² + 4

Front

Convert the equation y = x² + 4x into vertex form.

Back

y = (x + 2)² - 4