characteristic of quadratic graph

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

How do you determine if the vertex of a quadratic function is a minimum or maximum?

Back

If the coefficient of the x² term (a) is positive, the vertex is a minimum. If a is negative, the vertex is a maximum.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the axis of symmetry represent in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

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

Back

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

Front

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

Back

The coefficient 'a' 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 effect of changing the value of 'b' in the quadratic equation?

Back

Changing 'b' affects the position of the vertex along the x-axis and the axis of symmetry.

Front

What is the role of the constant 'c' in the quadratic equation?

Back

The constant 'c' represents the y-intercept of the quadratic function, which is the point where the graph intersects the y-axis.

Front

How do you convert a quadratic equation from vertex form to standard form?

Back

Expand the vertex form y = a(x - h)² + k to standard form by applying the distributive property and combining like terms.

Front

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

Back

The roots (or x-intercepts) are the points where the graph intersects the x-axis, and they can be found by factoring or using the quadratic formula.