Quadratic Key Features

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 does the y-value of the vertex represent in a quadratic function?

Back

The y-value of the vertex represents the maximum or minimum value of the function, depending on the direction of the parabola.

Front

What are x-intercepts in a quadratic graph?

Back

X-intercepts are the points where the graph intersects the x-axis, indicating the values of x for which y = 0.

Front

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

Back

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

Front

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

Back

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

Front

What is the axis of symmetry in a quadratic graph?

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

What does it mean if a quadratic function opens upwards?

Back

If a quadratic function opens upwards, it has a minimum point at the vertex, and the y-value of the vertex is the minimum value of the function.

Front

What does it mean if a quadratic function opens downwards?

Back

If a quadratic function opens downwards, it has a maximum point at the vertex, and the y-value of the vertex is the maximum value of the function.

Front

How can you determine if a vertex is a maximum or minimum?

Back

You can determine if a vertex is a maximum or minimum by looking at the leading coefficient (a) in the quadratic equation: if a > 0, it's a minimum; if a < 0, it's a maximum.

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.