graph the function $f(x) = -4x^2$. plot the vertex. then plot another point on the parabola. if you make a…

graph the function $f(x) = -4x^2$. 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 $f(x) = -4x^2$. 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: Identify the vertex

The function is in the form ( f(x) = ax^2 + bx + c ), for ( f(x) = -4x^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 ( x = 0 ). Substitute ( x = 0 ) into ( f(x) ): ( f(0)=-4(0)^2 = 0 ). So the vertex is at ( (0, 0) ).

Step2: Find another point

Let's choose ( x = 1 ). Substitute ( x = 1 ) into ( f(x)=-4x^2 ): ( f(1)=-4(1)^2=-4 ). So the point ( (1, - 4) ) is on the parabola. We could also choose ( x=- 1 ), ( f(-1)=-4(-1)^2=-4 ), so ( (-1, - 4) ) is also on the parabola. To graph the parabola, plot the vertex ( (0,0) ) and then plot the point ( (1, - 4) ) (or ( (-1, - 4) )) and draw a parabola opening downward (since ( a=-4<0 )) passing through these points.

Answer:

The vertex is at ((0, 0)) and another point (e.g., ((1, - 4)) or ((-1, - 4))) can be plotted to graph the parabola ( f(x)=-4x^2 ).