Quadratics Standard Form

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the shape of the graph of a quadratic function called?

Back

A parabola.

Front

What does the coefficient 'a' in the standard form of a quadratic function determine?

Back

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

Front

How do you find the vertex of a parabola given 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

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

Front

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

Back

The maximum value occurs at the vertex if the parabola opens downwards; the minimum value occurs at the vertex if it opens upwards.

Front

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

Back

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

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the value of c in the standard form.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you convert from standard form to vertex form?

Back

Complete the square on the quadratic expression.