Parabola of the form y=x²: Finding a stationary point

To solve this problem, we'll follow these steps:

• Step 1: Substitute the given value of $x$ into the equation.
• Step 2: Perform the calculation to find $y$.

Now, let's work through each step:
Step 1: The given equation is $y = x^2$. We need to substitute $x = 2$ into this equation.

Step 2: Substitute to get $y = (2)^2$. Calculate $2 \times 2 = 4$.

Therefore, the value of $y$ when $x = 2$ is $y = 4$.

Hence, the solution to the problem is $y = 4$.

To solve this problem, we'll follow these steps:

• Step 1: Set the equation of the function with the given point, $x^2 = 4$.
• Step 2: Solve for $x$ by taking the square root of both sides. This accounts for both the positive and negative solutions.
• Step 3: Evaluate the expression to find the solutions.

Now, let's work through each step:
Step 1: Set up the equation based on the given information:
We have $x^2 = 4$.

Step 2: Solve by taking the square root of both sides:
Taking the square root, we get $x = \pm\sqrt{4}$.

Step 3: Simplify to find the values of $x$:
The square root of 4 is 2, thus $x = 2$ and $x = -2$.

Therefore, the solutions for $x$ are $x = 2$ and $x = -2$.

The correct answer is choice Answers a + b, which corresponds to having solutions $x = 2$ and $x = -2$.

To solve this problem, let's find the steps required to determine $x$ when $y = 16$ in the function $y = x^2$:

• Step 1: Substitute the given $y$ into the equation to get $x^2 = 16$.
• Step 2: To solve $x^2 = 16$, take the square root of both sides, remembering to include both positive and negative roots. This yields $x = \pm\sqrt{16}$.
• Step 3: Simplify to find $x = \pm4$, which gives the solutions $x = 4$ and $x = -4$.

Thus, the value(s) of $x$ that satisfy $y = 16$ in the function $y = x^2$ are $x = 4$ and $x = -4$.

Therefore, the solution to the given problem is $x = 4, x = -4$.

To solve the problem, we will proceed with the following steps:

• Identify the provided equation and condition.
• Apply the square root property to solve the equation.
• Verify the solution with the given choices.

Step-by-step solution:

Step 1: Substitute $y = 36$ into the equation $y = x^2$, which gives:

$x^2 = 36$

Step 2: Solve for $x$ by taking the square root of both sides. Using the square root property, we have:

$x = \pm \sqrt{36}$

Since the square root of 36 is 6, we find that:

$x = \pm 6$

Therefore, the solutions to the equation are $x = 6$ and $x = -6$.

Thus, the value of $x$ for $y = 36$ in the function $y = x^2$ is $x = \pm 6$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the value given for $x$.
• Step 2: Substitute the given $x$ value into the function.
• Step 3: Calculate the resulting value for $y$.

Now, let's work through each step:
Step 1: The problem states that $x = 6$.
Step 2: Using the function $y = x^2$, we substitute $x = 6$.
Step 3: Perform the calculation: $y = 6^2$.

Calculating $6^2$, we get $36$.
Therefore, for the function $y = x^2$, when $x = 6$, the value of $y$ is $y = 36$.

Let's solve the problem by following these steps:

• Step 1: Identify the equation to solve.
• Step 2: Apply the square root to both sides of the equation.
• Step 3: Solve for both positive and negative values of $x$.

Step 1: We start with the equation derived from the function:
$x^2 = 25$

Step 2: To isolate $x$, we take the square root of both sides. Remember, the square root of a number can be both positive and negative:
$x = \pm \sqrt{25}$

Step 3: Simplify the square root:
$x = \pm 5$, which means $x = 5$ or $x = -5$

Therefore, the values of $x$ that satisfy $y = 25$ in the function $y = x^2$ are $x = 5$ and $x = -5$.

Looking at the choices given, the correct answer is:

$x=5,x=-5$

The problem requires us to find the value of $x$ for the function $y = x^2$ when $y = 8$.

Let's solve this step-by-step:

• Step 1: Set up the equation based on the given function:
  $\ y = x^2$ becomes $\ x^2 = 8$.
• Step 2: Solve for $x$ by taking the square root of both sides:

Since $\ x^2 = 8$, we take the square root of both sides to find $x$:

$x = \pm\sqrt{8}$

Step 3: Simplify the square root:

The square root of 8 can be simplified to $\ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}$.

Thus, $\ x = \pm 2\sqrt{2}$.

Therefore, the solution is $x = \pm 2\sqrt{2}$, which corresponds to choice 4.

To find the value of $y$ for the function $y = x^2$ at the point where $x = 10$, we will follow these steps:

• Step 1: Identify the function, which is $y = x^2$.
• Step 2: Substitute $x = 10$ into the function.
• Step 3: Perform the calculation to find $y$.

Now, let's work through each step:
Step 1: We have the function $y = x^2$.
Step 2: Substitute $x = 10$ into the equation: $y = (10)^2$.
Step 3: Calculate the result: $y = 10 \times 10 = 100$.

Therefore, the value of $y$ for the function when $x = 10$ is $y = 100$.

To find the value of $y$ when $x = 7$ in the function $y = x^2$, we will follow these straightforward steps:

• Step 1: Substitute $x = 7$ into the function. Therefore, $y = (7)^2$.
• Step 2: Calculate the value of $7^2$. The expression $7^2$ means $7 \times 7$.
• Step 3: Perform the multiplication. $7 \times 7 = 49$.

Thus, when $x = 7$, the value of $y$ is $49$.

Therefore, the value of $y$ at $x = 7$ is $y = 49$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information.
• Step 2: Apply the appropriate formula by substituting the given value.
• Step 3: Perform the calculation to find the solution.

Let's work through each step:

Step 1: The function is given by $y = x^2$ and the value of $x$ is 12.

Step 2: Substitute $x = 12$ into the function. We have:

$y = 12^2$.

Step 3: Calculate the square of 12:

$12^2 = 144$.

Therefore, the value of $y$ at the point $x = 12$ is $y = 144$.

Comparing this with the multiple-choice answers, the correct choice is:

• Choice 4: $y = 144$.

Thus, the final answer is $y = 144$.