Parabola y=x² Practice Problems with Step-by-Step Solutions

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 up the equation from the function definition.
• Step 2: Solve the equation by taking the square root of both sides.
• Step 3: Identify all possible values for $x$.
• Step 4: Compare with the given answer choices.

Now, let's work through each step:

Step 1: We start with the equation given by the function $f(x) = x^2$. We know $f(?) = 16$, so we can write:

$x^2 = 16$

Step 2: To solve for $x$, we take the square root of both sides of the equation:

$x = \pm \sqrt{16}$

Step 3: Solve for $\sqrt{16}$:

The square root of 16 is 4, so:

$x = 4$ or $x = -4$

This gives us the two solutions: $x = 4$ and $x = -4$.

Step 4: Compare these solutions to the answer choices. The correct choice is:

$f(4)$ and $f(-4)$

Therefore, the solution to the problem is $f(4)$ and $f(-4)$.

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 $y = 36$.

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

• Step 1: Set up the equation based on the function $f(x)=x^2$ for $f(?)=25$.
• Step 2: Solve for $x$ by applying the square root operation.

Now, let's work through each step:
Step 1: We start with the equation $x^2 = 25$ derived from $f(x) = 25$.
Step 2: To solve for $x$, we take the square root of both sides:

$x = \pm \sqrt{25}$

Calculating the square root gives us $x = \pm 5$. However, we are looking for a specific point that fits one of the answer choices:
Therefore, the solution based on the choices provided is $x = 5$.

Concluding, the missing value of the function point is $f(5)$, which coincides with choice 1.

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

• Step 1: Set up the equation $x^2 = 9$.
• Step 2: Solve for $x$ by taking the square root of both sides.
• Step 3: Choose the correct answer from the given options.

Now, let's work through each step:
Step 1: We set $x^2 = 9$.
Step 2: Solving for $x$, we take the square root of both sides: $x = \pm \sqrt{9}$.
Step 3: This yields two solutions: $x = 3$ and $x = -3$.

Comparing these values with the given choices:

• Choice 1: $f(3)$ corresponds to $x = 3$.
• Choice 3: $f(-3)$ corresponds to $x = -3$.

Both choices $f(3)$ and $f(-3)$ are correct, leading us to select the combined choice: Answer A+C.