Quadratics - Standard Form

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

What is the significance of the vertex in a parabola?

Back

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

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

If 'a' is positive, the function has a minimum value at the vertex; if 'a' is negative, it has a maximum value.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0) = c in the standard form.

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, find the vertex, axis of symmetry, y-intercept, and plot additional points, then draw a smooth curve.

Front

What is the effect of changing the value of 'b' in a quadratic equation?

Back

Changing 'b' affects the position of the vertex and the axis of symmetry, but does not change the direction of the parabola.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by D = b² - 4ac and determines the nature of the roots: if D > 0, two real roots; D = 0, one real root; D < 0, no real roots.