Final answer:
The 'look fors' for the y-value of the vertex in intercept form involves simply identifying the k-value from y = a(x-h)^2 + k, whereas in standard form y = ax^2 + bx + c, you must calculate the vertex's y-value by first using the formula -b/(2a) for the x-value and substituting back into the equation.
Step-by-step explanation:
The vertex form of a quadratic equation and the standard form are different representations that can be used to identify the vertex of a parabola. In the vertex form of a quadratic equation, y = a(x-h)^2 + k, the vertex (h, k) can be clearly seen from the equation itself, where h and k are the x-value and y-value of the vertex, respectively.
In contrast, the standard form of a quadratic equation is y = ax^2 + bx + c. To find the x-value of the vertex, the formula -b/(2a) can be used. Once the x-value is found, it needs to be plugged back into the equation to find the corresponding y-value. The y-value of the vertex in standard form is not directly visible from the equation, unlike in the vertex form.
Understanding the slope and y-intercept for a linear equation y = a + bx can help predict the behavior of linear models. The coefficient of x, which represents the slope, influences the steepness of the line. The constant value a, which is the y-intercept, determines where the line crosses the y-axis. In situations where a line has a larger y-intercept, graphically, it would shift up from the original origin, introducing a vertical translation.