Parabola y=(x-p)² Practice Problems with Solutions

To solve this problem, we will find the intersection of the function with the Y-axis by following these steps:

• Step 1: Recognize that the intersection with the Y-axis occurs where $x = 0$.
• Step 2: Substitute $x = 0$ into the function $y = (x+4)^2$.
• Step 3: Perform the calculation to find the y-coordinate.

Now, let's solve the problem:

Step 1: Identify the Y-axis intersection by setting $x = 0$.
Step 2: Substitute $x = 0$ into the function:

$y = (0+4)^2 = 4^2 = 16$

Step 3: The intersection point on the Y-axis is $(0, 16)$.

Therefore, the solution to the problem is $(0, 16)$.

To solve this problem, we'll find the intersection of the function $y = (x-2)^2$ with the x-axis. The x-axis is characterized by $y = 0$. Hence, we set $(x-2)^2 = 0$ and solve for $x$.

Let's follow these steps:

• Step 1: Set the function equal to zero:

$(x-2)^2 = 0$

• Step 2: Solve the equation for $x$:

Taking the square root of both sides gives $x - 2 = 0$.

Adding 2 to both sides results in $x = 2$.

• Step 3: Find the intersection point coordinates:

The x-coordinate is $x = 2$, and since it intersects the x-axis, the y-coordinate is $y = 0$.

Therefore, the intersection point of the function with the x-axis is $(2, 0)$.

The correct choice from the provided options is $(2, 0)$.

To determine if the given statement is true, consider the equation of the parabola $y = (x - p)^2$. The y-intercept occurs where the parabola crosses the y-axis, which is at $x = 0$.

Step 1: Substitute $x = 0$ into the equation:

$y = (0 - p)^2 = p^2$

Step 2: Calculate the y-intercept:

The y-intercept of the parabola is $y = p^2$.

Conclusion: The statement "To find the y-axis intercept, you substitute $x = 0$ into the equation and solve for $y$" is indeed True, as applying this method correctly determined the y-intercept for the given form of a parabola. Therefore, the answer to the problem is True.

To solve this problem, let's go through the process of elimination to find the graph corresponding to $y = x^2$.

The function $y = x^2$ is an upward-opening parabola with its vertex located at the origin point (0, 0). It is symmetric about the y-axis.

Based on our problem statements or diagrams, the given function will match with chart '2'. This chart will depict an upward-facing parabolic shape with no horizontal or vertical shifts.

Therefore, the solution to the problem is the chart labeled 2.

To solve this problem, we need to determine whether substituting $x = 0$ gives us the points of intersection with the x-axis for the parabola $y = (x - p)^2$.

To find the x-intercepts of any function, we set $y = 0$ because the x-intercepts occur where the curve meets the x-axis, which implies a zero output or function value:

• Start with the equation: $y = (x - p)^2$.
• Set $y = 0$ for the x-intercept: $(x - p)^2 = 0$.
• Solving this gives $(x - p) = 0$, which simplifies to $x = p$.
• Thus, the x-intercept happens at the point where $x = p$, not where $x = 0$.

Therefore, substituting $x = 0$ does not provide the x-intercepts. Instead, it provides the y-intercept. Therefore, the statement given in the problem is False.

Thus, the solution to the problem is False.