Question

graph the function f(x) = 7x² - 4. 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: Identify the vertex form

The quadratic function is given as \( f(x) = 7x^2 - 4 \). The vertex form of a quadratic function is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex. Here, \( h = 0 \) (since there is no \( x \)-term inside the square) and \( k = -4 \). So the vertex is \((0, -4)\).

Step2: Find another point

Let's choose \( x = 1 \). Substitute \( x = 1 \) into the function: \( f(1) = 7(1)^2 - 4 = 7 - 4 = 3 \). So the point \((1, 3)\) is on the parabola. (We could also choose \( x = -1 \), and since the parabola is symmetric about the y - axis, \( f(-1)=7(-1)^2 - 4 = 3 \), so \((-1, 3)\) is also on the parabola.)

Step3: Plot the points

First, plot the vertex \((0, -4)\) on the coordinate plane. Then plot the point \((1, 3)\) (or \((-1, 3)\)). After plotting these two points, we can draw the parabola (a U - shaped curve) since for a quadratic function \( y = ax^2+bx + c \) with \( a>0 \) (here \( a = 7>0 \)), the parabola opens upwards.

Answer:

Vertex: \((0, -4)\), Another point: \((1, 3)\) (or \((-1, 3)\)) (and the parabola is drawn through these points)