graph the function f(x) = 4x² + 8x - 4. plot the vertex. then plot another point on the parabola. if you…

graph the function f(x) = 4x² + 8x - 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.

graph the function f(x) = 4x² + 8x - 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.

Answer

Explanation:

Step1: Find the x - coordinate of the vertex

For a quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex is given by $x=-\frac{b}{2a}$. In the function $f(x)=4x^{2}+8x - 4$, where $a = 4$ and $b = 8$. So, $x=-\frac{8}{2\times4}=-\frac{8}{8}=- 1$.

Step2: Find the y - coordinate of the vertex

Substitute $x=-1$ into the function $f(x)=4x^{2}+8x - 4$. Then $f(-1)=4\times(-1)^{2}+8\times(-1)-4=4 - 8 - 4=-8$. So the vertex is $(-1,-8)$.

Step3: Find another point

Let's choose $x = 0$. Substitute $x = 0$ into the function $f(x)=4x^{2}+8x - 4$. Then $f(0)=4\times0^{2}+8\times0 - 4=-4$. So another point is $(0,-4)$.

Answer:

Vertex: $(-1,-8)$; Another point: $(0,-4)$