Question

graph the function f(x) = 2x² - 10. 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 vertex form

The quadratic function is \( f(x) = 2x^2 - 10 \), which is in the form \( f(x) = ax^2 + k \). For such a form, the vertex is at \( (0, k) \). Here, \( k = -10 \), so the vertex is \( (0, -10) \).

Step2: Find another point

Let's choose \( x = 1 \). Substitute into \( f(x) \): \( f(1) = 2(1)^2 - 10 = 2 - 10 = -8 \). So the point \( (1, -8) \) is on the parabola. (We could also choose \( x = 2 \): \( f(2) = 2(4) - 10 = 8 - 10 = -2 \), giving \( (2, -2) \), etc.)

Answer:

Vertex: \( (0, -10) \), Another point: \( (1, -8) \) (or other valid point like \( (2, -2) \))