Graphing Quadratics

Front

What is the vertex of the quadratic function y = x² - 8x + 14?

Back

(4, -2)

Front

What are the green dots called in a parabola?

Back

roots or x-intercepts

Front

How does the parabola open for the equation y = -x² + 4x - 1?

Back

down

Front

What is the y-intercept of the equation y = 2x² + 8x + 3?

Back

(0, 3)

Front

What is the domain of all quadratic functions?

Back

All real numbers

Front

What is the standard form of a quadratic function?

Back

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

Front

What does the coefficient 'a' determine in a quadratic function?

Back

The direction in which the parabola opens (upward if a > 0, downward if a < 0).

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

How do you find the roots of a quadratic equation?

Back

By using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

It determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.