E. Writing the Equation of the Function
Completion requirements
E. Writing the Equation of the Function
What characteristics of the graph of a quadratic function will help determine its equation? Given the graph of a quadratic function, there are up to four coordinates that should be quick to determine: the vertex, \(x\)-intercept(s), and \(y\)-intercept.
The vertex gives the values of \(p\) and \(q\). (Recall that the vertex coordinates are \((p, q)\).) To determine \(a\), you must have a second point other than the vertex. Fortunately, you will have up to three others to choose from (the \(x\)- and \(y\)-intercepts). Substitute the coordinates of the second point into the equation of the function, and solve for \(a\). Example 1 will demonstrate this.
The vertex gives the values of \(p\) and \(q\). (Recall that the vertex coordinates are \((p, q)\).) To determine \(a\), you must have a second point other than the vertex. Fortunately, you will have up to three others to choose from (the \(x\)- and \(y\)-intercepts). Substitute the coordinates of the second point into the equation of the function, and solve for \(a\). Example 1 will demonstrate this.