Graphing Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form of y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic equation look like?

Back

The graph of a quadratic equation is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens downwards or upwards.

Front

How do you determine if a parabola has a maximum or minimum?

Back

If the coefficient 'a' in the quadratic equation is positive, the parabola opens upwards and has a minimum. If 'a' is negative, it opens downwards and has a maximum.

Tags

CCSS.HSF-IF.C.7A

Front

What is the axis of symmetry in a quadratic equation?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

How do you find the axis of symmetry for the equation y = x² + 2?

Back

For the equation y = x² + 2, the axis of symmetry is x = 0.

Front

What is the formula to find the vertex of a parabola?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

What is the vertex of the function f(x) = -x² - 4x + 12?

Back

The vertex of the function is (-2, 16).

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it indicates that the quadratic function has a minimum value at its vertex.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it indicates that the quadratic function has a maximum value at its vertex.

Tags

CCSS.HSF-IF.C.7A