Question

graph the function f(x) = -x². 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 of the parabola

The quadratic function is given in the form \( f(x) = -x^2 \), which can be written as \( f(x) = -1(x - 0)^2 + 0 \). For a quadratic function in vertex form \( f(x) = a(x - h)^2 + k \), the vertex is at \( (h, k) \). Here, \( h = 0 \) and \( k = 0 \), so the vertex is at \( (0, 0) \).

Step2: Find another point on the parabola

Let's choose \( x = 1 \). Substitute \( x = 1 \) into the function \( f(x) = -x^2 \). Then \( f(1) = -(1)^2 = -1 \). So the point \( (1, -1) \) lies on the parabola. Similarly, if we choose \( x = -1 \), \( f(-1) = -(-1)^2 = -1 \), so \( (-1, -1) \) is also on the parabola. We can plot the vertex \( (0, 0) \) and then another point like \( (1, -1) \) or \( (-1, -1) \) to draw the parabola, which opens downward because the coefficient of \( x^2 \) is negative.

Answer:

The vertex is at \((0, 0)\), and another point on the parabola can be \((1, -1)\) (or \((-1, -1)\) etc.). To graph, plot \((0, 0)\) as the vertex and then a point like \((1, -1)\) and draw the downward - opening parabola passing through these points.