Question

graph the parabola.
y = x² - 8x + 12
plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. then click on the graph - a function button.

Explanation:

Step1: Find the vertex

For a parabola \( y = ax^2 + bx + c \), the x - coordinate of the vertex is \( x=-\frac{b}{2a} \). For \( y = x^{2}-8x + 12 \), \( a = 1 \), \( b=-8 \). So \( x=-\frac{-8}{2\times1}=4 \). Substitute \( x = 4 \) into the equation: \( y=4^{2}-8\times4 + 12=16-32 + 12=-4 \). The vertex is \( (4,-4) \).

Step2: Find points to the left of the vertex

Let's choose \( x = 2 \): \( y=2^{2}-8\times2 + 12=4-16 + 12=0 \). So the point is \( (2,0) \).
Let's choose \( x = 3 \): \( y=3^{2}-8\times3 + 12=9-24 + 12=-3 \). So the point is \( (3,-3) \).

Step3: Find points to the right of the vertex

Let's choose \( x = 5 \): \( y=5^{2}-8\times5 + 12=25-40 + 12=-3 \). So the point is \( (5,-3) \).
Let's choose \( x = 6 \): \( y=6^{2}-8\times6 + 12=36-48 + 12=0 \). So the point is \( (6,0) \).

Answer:

Vertex: \( (4,-4) \), Left points: \( (2,0) \), \( (3,-3) \), Right points: \( (5,-3) \), \( (6,0) \) (These are the five points to plot on the parabola)