Graphing Quadratics

Front

What does it mean if a parabola opens down?

Back

The coefficient of the x² term in the quadratic equation is negative.

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c, where a, b, and c are constants.

Front

How do you determine the direction a parabola opens?

Back

If 'a' (the coefficient of x²) is positive, it opens up; if 'a' is negative, it opens down.

Front

What is the axis of symmetry in a parabola?

Back

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

Front

What are the roots or x-intercepts of a quadratic function?

Back

The points where the parabola intersects the x-axis, found by solving the equation y = 0.

Front

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

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 parabola y = x² - 4x + 5?

Back

(2, 1) is the vertex.

Front

What is the formula for the vertex of a parabola in standard form?

Back

The vertex is given by (h, k) where h = -b/(2a) and k = f(h).

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

There are two distinct real roots.