M II 5.1.5 What do you know from Intercept form?

Front

What is the intercept form of a quadratic function?

Back

The intercept form of a quadratic function is given by y = a(x - p)(x - q), where p and q are the x-intercepts of the parabola.

Front

How do you find the zeros of a quadratic function in intercept form?

Back

To find the zeros of a quadratic function in intercept form, set the function equal to zero and solve for x: 0 = a(x - p)(x - q). The solutions will be x = p and x = q.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function is a vertical line that passes through the vertex of the parabola, and it can be found using the formula x = (p + q) / 2, where p and q are the x-intercepts.

Front

How do you determine the vertex of a parabola given its intercept form?

Back

The vertex of a parabola in intercept form y = a(x - p)(x - q) can be found at the point x = (p + q) / 2, and then substituting this x-value back into the function to find the corresponding y-value.

Front

What are x-intercepts in the context of a quadratic function?

Back

X-intercepts are the points where the graph of the quadratic function crosses the x-axis, and they can be found by solving the equation f(x) = 0.

Front

What does the parameter 'a' represent in the intercept form of a quadratic function?

Back

The parameter 'a' in the intercept form y = a(x - p)(x - q) determines the direction and width of the parabola. If a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

How can you verify the axis of symmetry using the x-intercepts?

Back

You can verify the axis of symmetry by calculating the average of the x-intercepts: x = (p + q) / 2. This value should be the same as the x-coordinate of the vertex.

Front

What is the significance of the x-intercepts in a quadratic function?

Back

The x-intercepts indicate the solutions to the equation f(x) = 0, and they represent the points where the function changes sign.

Front

How do you convert a quadratic function from standard form to intercept form?

Back

To convert from standard form f(x) = ax^2 + bx + c to intercept form y = a(x - p)(x - q), you can factor the quadratic expression or use the quadratic formula to find the x-intercepts.

Front

What is the relationship between the axis of symmetry and the vertex of a parabola?

Back

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