Question

1. graph the function f(x) = (x - 4)² + 8 and identify its vertex.

vertex: ____________

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a quadratic function is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

Step2: Identify h and k from given function

For the function \( f(x) = (x - 4)^2 + 8 \), comparing with \( a(x - h)^2 + k \), we have \( h = 4 \) and \( k = 8 \). So the vertex is \((4, 8)\). To graph the function, we know it's a parabola opening upwards (since \( a = 1>0 \)) with vertex at \((4, 8)\). We can plot the vertex and then find other points by substituting x - values (e.g., x = 3: \( f(3)=(3 - 4)^2+8 = 1 + 8 = 9 \); x = 5: \( f(5)=(5 - 4)^2+8 = 1 + 8 = 9 \)) and draw the parabola.

Answer:

The vertex of the function \( f(x)=(x - 4)^2 + 8 \) is \((4, 8)\). For the graph, plot the vertex at \((4, 8)\), and since it's a parabola opening upwards (coefficient of \((x - 4)^2\) is positive), plot symmetric points around x = 4 (e.g., (3, 9) and (5, 9), (2, 12) and (6, 12) etc.) and draw the curve. The vertex is \(\boldsymbol{(4, 8)}\).