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: 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 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: 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 $x = 4, x = -4$.