Quadratics Review Game

Front

What is a parabola?

Back

A parabola is a symmetrical, curved shape that represents the graph of a quadratic function. It can open upwards or downwards depending on the coefficient of the x² term.

Front

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

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

Identify the vertex of the parabola represented by the equation f(x) = ax² + bx + c.

Back

The vertex of the parabola can be found using the formula x = -b/(2a). This gives the x-coordinate of the vertex, and substituting this value back into the equation gives the y-coordinate.

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.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if it's positive, there are two distinct real roots; if it's zero, there is one real root; if it's negative, there are no real roots.

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. It can be found using the formula x = -b/(2a).

Front

How can you determine the number of solutions from a graph of a quadratic function?

Back

The number of solutions corresponds to the number of times the graph intersects the x-axis: two intersections mean two solutions, one intersection means one solution, and no intersections mean no solutions.

Front

What is the vertex form of a quadratic equation?

Back

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