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 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 $y = 36$.

The problem asks us to find an $x$ such that in the function $y = x^2$, the value of $y$ becomes 16. To do this, we'll substitute $y = 16$ into the equation and solve for $x$.

1. Start with the equation of the function:

$y = x^2$

2. Substitute $y = 16$ into the equation:

$16 = x^2$

3. Solve $x^2 = 16$ for $x$:

• Take the square root of both sides to solve for $x$:
• $x = \pm \sqrt{16}$
• This gives $x = 4$ or $x = -4$

4. Identify the points on the function for these values of $x$:

• For $x = 4$, the point is $(4, 16)$.
• For $x = -4$, the point is $(-4, 16)$, but this is not provided in the choice list.

Among the given options, the point we find in the choices is:

$(4, 16)$

Therefore, the correct answer is the choice that corresponds with this point:

$(4,16)$