graph the function $f(x) = -5x^2$. plot the vertex. then plot another point on the parabola. if you make a…

graph the function $f(x) = -5x^2$. 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.

graph the function $f(x) = -5x^2$. 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.

Answer

Explanation:

Step1: Find the vertex

For a quadratic function ( f(x) = ax^2 + bx + c ), the vertex is at ( x = -\frac{b}{2a} ). In ( f(x) = -5x^2 ), ( b = 0 ), ( a = -5 ). So ( x = -\frac{0}{2\times(-5)} = 0 ). Substitute ( x = 0 ) into ( f(x) ), ( f(0) = -5\times0^2 = 0 ). So the vertex is ( (0, 0) ).

Step2: Find another point

Let's choose ( x = 1 ). Substitute ( x = 1 ) into ( f(x) ): ( f(1) = -5\times1^2 = -5 ). So the point ( (1, -5) ) is on the parabola. (We could also choose ( x = -1 ), since the function is even, ( f(-1) = -5\times(-1)^2 = -5 ), so ( (-1, -5) ) is also on the parabola.)

Answer:

The vertex is at ( (0, 0) ), and another point (e.g., ( (1, -5) ) or ( (-1, -5) )) can be plotted to draw the parabola opening downward with vertex at the origin and passing through the chosen point.