Graphing Quadratic Equations

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a'.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

How do you find the axis of symmetry of a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

What is the range of a quadratic function that opens upwards?

Back

The range of a quadratic function that opens upwards is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range of a quadratic function that opens downwards is all real numbers less than or equal to the y-coordinate of the vertex.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating f(0).

Front

How can you determine if a quadratic function has real roots?

Back

You can determine if a quadratic function has real roots by calculating the discriminant (D = b² - 4ac). If D > 0, there are two real roots; if D = 0, there is one real root; if D < 0, there are no real roots.