Quadratic Graphs

Front

What is the vertex of a quadratic graph?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, represented as (h, k) in the vertex form y = a(x - h)² + k.

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the graph into two mirror-image halves, given by the equation x = h, where (h, k) is the vertex.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How can you determine if a quadratic graph has a maximum or minimum value?

Back

If the coefficient 'a' in the standard form y = ax² + bx + c is positive, the graph opens upwards and has a minimum value. If 'a' is negative, the graph opens downwards and has a maximum value.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the quadratic function, indicating the highest or lowest value of the function.

Front

How do you find the axis of symmetry from a quadratic equation in standard form?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are the coefficients from the standard form y = ax² + bx + c.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the graph (narrower if |a| > 1, wider if |a| < 1).

Front

What is the role of the 'b' value in a quadratic equation?

Back

The 'b' value affects the position of the vertex along the x-axis and influences the axis of symmetry.

Front

What is the role of the 'c' value in a quadratic equation?

Back

The 'c' value represents the y-intercept of the quadratic graph, indicating where the graph crosses the y-axis.

Front

How can you identify the vertex from a quadratic equation in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h), substituting h back into the equation.