Quadratics Review

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is given by: y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the vertex of the parabola from the equation y = a(x - h)² + k?

Back

The vertex of the parabola is the point (h, k) in the equation y = a(x - h)² + k.

Front

What is the y-intercept of a quadratic equation?

Back

The y-intercept of a quadratic equation is the point where the graph intersects the y-axis, found by setting x = 0 in the equation.

Front

How do you factor the quadratic expression x² - bx + c?

Back

To factor the expression, find two numbers that multiply to c and add to -b, then express it as (x - p)(x - q) where p and q are the two numbers.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by: y = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The 'a' value indicates the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the axis of symmetry in a parabola?

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) for the standard form.

Front

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

Back

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

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the roots of a quadratic equation and is given by: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots.