key features of quadratics

Front

What are the coordinates of the y-intercept of a quadratic function?

Back

(0, c) where c is the constant term in the quadratic equation y = ax^2 + bx + c.

Front

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

Back

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

Front

How do you determine the x-intercepts of a quadratic function from its graph?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by setting y = 0.

Front

What does it mean if a quadratic graph has a minimum value?

Back

The vertex of the parabola is the lowest point on the graph, indicating the function opens upwards.

Front

What are the x-intercepts of the quadratic function y = x^2 - 4?

Back

(2, 0) and (-2, 0) are the x-intercepts.

Front

What is the standard form of a quadratic equation?

Back

y = ax^2 + bx + c where a, b, and c are constants.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, given by the coordinates (h, k) in the vertex form y = a(x-h)^2 + k.

Front

How can you find the y-intercept of a quadratic function?

Back

Set x = 0 in the quadratic equation and solve for y.

Front

What does the 'a' value in a quadratic equation indicate about the graph?

Back

If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: two real roots, one real root, or no real roots.