In finding the vertex from intercept form, how do you find the y-coordinate?

In finding the vertex from intercept form, how do you find the y-coordinate?

• A. y=f((r1+r2)/2)
• B. y=(r1+r2)/2
• C. y=f(r1)/f(r2)
• D. y=f(r1+r2)

Answer: (A)

To find the y-coordinate of the vertex from the intercept form of a quadratic function, which is typically represented as \(y = a(x - r_1)(x - r_2)\), where \(r_1\) and \(r_2\) are the x-intercepts, the first step is to determine the x-coordinate of the vertex. This can be found by averaging the two intercepts: \(x = \frac{r_1 + r_2}{2}\). Once you have the x-coordinate of the vertex, you substitute this value back into the original quadratic function \(f(x)\) to find the corresponding y-coordinate. This means that the correct approach is to evaluate the function at the average of the roots, which gives us \(y = f\left(\frac{r_1 + r_2}{2}\right)\). Thus, the choice that correctly describes the method for finding the y-coordinate of the vertex is indeed that you substitute the average of the roots into the function \(f\), resulting in the expression \(y = f\left(\frac{r_1 + r_2}{2}\right)\). This relational formula effectively yields the vertex's y-coordinate based on the properties of

To find the y-coordinate of the vertex from the intercept form of a quadratic function, which is typically represented as (y = a(x - r_1)(x - r_2)), where (r_1) and (r_2) are the x-intercepts, the first step is to determine the x-coordinate of the vertex. This can be found by averaging the two intercepts: (x = \frac{r_1 + r_2}{2}).

Once you have the x-coordinate of the vertex, you substitute this value back into the original quadratic function (f(x)) to find the corresponding y-coordinate. This means that the correct approach is to evaluate the function at the average of the roots, which gives us (y = f\left(\frac{r_1 + r_2}{2}\right)).

Thus, the choice that correctly describes the method for finding the y-coordinate of the vertex is indeed that you substitute the average of the roots into the function (f), resulting in the expression (y = f\left(\frac{r_1 + r_2}{2}\right)). This relational formula effectively yields the vertex's y-coordinate based on the properties of