Quadratic Graph Properties - Lab

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. It can be found using the formula x = -b/(2a) for a quadratic equation in the form ax^2 + bx + c.

Front

How do you determine the vertex of a parabola from its equation?

Back

The vertex of a parabola given by the equation y = ax^2 + bx + c can be found using the formula (-b/(2a), f(-b/(2a))) where f(x) is the function.

Front

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

Back

The vertex represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards. It is the point where the graph changes direction.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the x-values where the graph intersects the x-axis. They can be found by solving the equation ax^2 + bx + c = 0.

Front

How can you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function can be found at the vertex. If the parabola opens upwards, the vertex gives the minimum value; if it opens downwards, it gives the maximum value.

Front

What does it mean if a quadratic graph has no real zeros?

Back

If a quadratic graph has no real zeros, it means the parabola does not intersect the x-axis. This occurs when the discriminant (b^2 - 4ac) is less than zero.

Front

How do you identify the direction in which a parabola opens?

Back

The direction of a parabola is determined by the coefficient 'a' in the quadratic equation y = ax^2 + bx + c. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the formula for the axis of symmetry in a quadratic function?

Back

The formula for the axis of symmetry is x = -b/(2a), where 'a' and 'b' are the coefficients from the quadratic equation in standard form.

Front

How can you graph a quadratic function?

Back

To graph a quadratic function, find the vertex, axis of symmetry, and zeros. Plot these points and draw a smooth curve through them, ensuring the correct direction of the parabola.

Front

What is the relationship between the coefficients of a quadratic equation and its graph?

Back

The coefficients 'a', 'b', and 'c' in the quadratic equation y = ax^2 + bx + c affect the shape, position, and direction of the parabola.