Question

graph the parabola.
y=3x^2
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

The equation of the parabola is \( y = 3x^2 \). For a parabola in the form \( y = ax^2+bx + c \), the vertex is at \( x=-\frac{b}{2a} \). Here, \( a = 3 \), \( b = 0 \), so \( x = 0 \). Substituting \( x = 0 \) into the equation, we get \( y=3(0)^2 = 0 \). So the vertex is \( (0,0) \).

Step2: Find points to the left of the vertex

Let's choose \( x=-1 \) and \( x = - 2 \).

• For \( x=-1 \): \( y = 3(-1)^2=3(1) = 3 \). So the point is \( (-1,3) \).
• For \( x=-2 \): \( y = 3(-2)^2=3(4)=12 \). So the point is \( (-2,12) \).

Step3: Find points to the right of the vertex

Let's choose \( x = 1 \) and \( x=2 \).

• For \( x = 1 \): \( y=3(1)^2 = 3 \). So the point is \( (1,3) \).
• For \( x = 2 \): \( y=3(2)^2=3(4) = 12 \). So the point is \( (2,12) \).

To graph the parabola, plot the vertex \( (0,0) \), the points to the left \( (-1,3) \), \( (-2,12) \) and the points to the right \( (1,3) \), \( (2,12) \) and then draw a smooth curve through these points.

Answer:

The five points are the vertex \((0,0)\), two points to the left \((-1,3)\), \((-2,12)\) and two points to the right \((1,3)\), \((2,12)\). Plot these points and draw the parabola \( y = 3x^2 \) through them.