Which of the following is the
intersection point of
16 with the axis?

Ask by Williams Henry. in the United States

Dec 02,2024

Question

Which of the following is the intersection point of $$ y=x^{\wedge} 2+6 x- $$ 16 with the $$ x- $$ axis?

UpStudy AI · Accepted Answer

To find the intersection point of the curve $$ y=x^2+6x-16 $$ with the x-axis, we need to set $$ y $$ to 0 and solve for $$ x $$.

Given equation: $$ y=x^2+6x-16 $$

Setting $$ y $$ to 0:
$$ 0 = x^2 + 6x - 16 $$

Now, we need to solve this quadratic equation to find the x-coordinate of the intersection point with the x-axis. Let's solve this equation.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$x^{2}+6x-16=0$$
- step1: Factor the expression:
  $$\left(x-2\right)\left(x+8\right)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&x-2=0\&x+8=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=2\&x=-8\end{align}$$
- step4: Rewrite:
  $$x_{1}=-8,x_{2}=2$$
The solutions to the equation $$ x^2 + 6x - 16 = 0 $$ are $$ x = -8 $$ and $$ x = 2 $$.

Therefore, the intersection points of the curve $$ y=x^2+6x-16 $$ with the x-axis are at $$ x = -8 $$ and $$ x = 2 $$.
The intersection points with the x-axis are at $$ x = -8 $$ and $$ x = 2 $$.

Which of the following is the
intersection point of
16 with the axis?

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Which of the following is the intersection point of 16 with the axis?