Formative: Exploring Quadratics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form of f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on the direction of the parabola.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What is the zero property of multiplication?

Back

The zero property of multiplication states that any number multiplied by zero equals zero, expressed as a * 0 = 0.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts of a quadratic function, set the function equal to zero and solve for x.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, representing the value of the function when x = 0.

Front

What is the factored form of a quadratic function?

Back

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

Front

What does it mean for a quadratic equation to have real roots?

Back

A quadratic equation has real roots if its discriminant (b^2 - 4ac) is greater than or equal to zero.

Front

How can you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if the leading coefficient (a) is positive and downwards if it is negative.

Front

What is the quadratic formula?

Back

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