Question

graph the function f(x) = 7x². plot the vertex. then plot another point on the parabola. if you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Explanation:

Step1: Find the vertex of the parabola

The function is in the form \( f(x) = ax^2 + bx + c \), for \( f(x) = 7x^2 \), \( b = 0 \), \( c = 0 \). The vertex of a parabola \( y = ax^2 + bx + c \) is at \( (-\frac{b}{2a}, f(-\frac{b}{2a})) \). Since \( b = 0 \), the x - coordinate of the vertex is \( -\frac{0}{2\times7}=0 \). Substitute \( x = 0 \) into \( f(x) \), we get \( f(0)=7\times0^2 = 0 \). So the vertex is \( (0,0) \).

Step2: Find another point on the parabola

Let's choose \( x = 1 \). Substitute \( x = 1 \) into \( f(x)=7x^2 \), we get \( f(1)=7\times1^2 = 7 \). So the point \( (1,7) \) is on the parabola. We can also choose \( x=- 1 \), \( f(-1)=7\times(-1)^2 = 7 \), so \( (-1,7) \) is also on the parabola. To plot the graph, first plot the vertex \( (0,0) \), then plot a point like \( (1,7) \) (or \( (-1,7) \)) and draw the parabola opening upwards (since \( a = 7>0 \)) passing through these points.

Answer:

The vertex is at \( (0,0) \), and another point on the parabola can be \( (1,7) \) (or \( (-1,7) \)). When graphing, plot \( (0,0) \) as the vertex and then a point such as \( (1,7) \) (or \( (-1,7) \)) and draw the parabola.