Graphing Quadratics

Front

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

Back

x = -b/(2a), where a and b are coefficients from the quadratic equation ax² + bx + c.

Front

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

Back

The values of x where the graph intersects the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the vertex of a parabola?

Back

The highest or lowest point on the graph of a quadratic function, located at (h, k) in the vertex form y = a(x-h)² + k.

Front

How do you find the x-intercepts of the quadratic equation y = x² - 4?

Back

Set y = 0: 0 = x² - 4, then factor to find x = 2 and x = -2.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the 'a' value in a quadratic equation determine?

Back

The direction of the parabola (opens upwards if a > 0, downwards if a < 0) and the width of the parabola.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: two real roots if > 0, one real root if = 0, and no real roots if < 0.

Front

How do you factor the quadratic expression n² - 13n + 40?

Back

(n - 5)(n - 8) is the factored form.

Front

What is the maximum or minimum value of a quadratic function?

Back

The y-coordinate of the vertex; maximum if the parabola opens downwards, minimum if it opens upwards.

Front

What is the vertex form of a quadratic equation?

Back

y = a(x - h)² + k, where (h, k) is the vertex.