B4/5 Quadratic Functions Review

Front

What is the vertex of a quadratic function?

Back

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

Front

What does it mean for a quadratic function to open upwards?

Back

A quadratic function opens upwards if the coefficient of x² is positive (a > 0), indicating a minimum point at the vertex.

Front

What does it mean for a quadratic function to open downwards?

Back

A quadratic function opens downwards if the coefficient of x² is negative (a < 0), indicating a maximum point at the vertex.

Front

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

Back

You determine this by looking at the sign of the coefficient of x²: if it's positive, the function has a minimum; if it's negative, it has a maximum.

Front

What are x-intercepts of a quadratic function?

Back

X-intercepts are the points where the graph of the function crosses the x-axis, found by setting y = 0 and solving for x.

Front

What are y-intercepts of a quadratic function?

Back

Y-intercepts are the points where the graph of the function crosses the y-axis, found by evaluating the function at x = 0.

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

For a quadratic in standard form y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a) and then substituting x back into the equation to find y.

Front

What is the significance of the discriminant in a quadratic equation?

Back

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

Front

What is the vertex form of a quadratic function?

Back

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