Solve y=x² When y=25: Finding the X-Value

Q: Why are there two answers for x when y = 25?

Because squaring eliminates the sign! Both $ 5^2 $ and $ (-5)^2 $ equal 25. When you reverse the process by taking the square root, you must consider both possibilities.

Q: How do I remember to include both positive and negative solutions?

Always write the ± symbol immediately when taking square roots: $ x = ±\sqrt{25} $. This reminds you that square roots have two values!

Q: What does the graph of y = x² look like at y = 25?

The parabola $ y = x^2 $ opens upward. At $ y = 25 $, a horizontal line crosses the parabola at exactly two points: $ (5, 25) $ and $ (-5, 25) $.

Q: Can x² ever equal a negative number?

No! Squaring any real number (positive or negative) always gives a positive result. So $ x^2 = -25 $ has no real solutions.

Quadratic Functions with Positive/Negative Solutions

What is the value of X for the function?

$y=x^2$

of the point $y=25$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 First, let's set up the problem and find the solution.

00:10 Insert the given numbers where needed, and solve for the variable X.

00:17 Now, we'll extract the root of the number.

00:22 Remember, when extracting a root, there are two answers: one positive and one negative.

00:35 And that's how we find the solution to this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the value of X for the function?

$y=x^2$

of the point $y=25$ ?

Step-by-step solution

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:

$x=5,x=-5$

Final Answer

$x=5,x=-5$

Key Points to Remember

Essential concepts to master this topic

Rule: Square root of both sides gives positive and negative solutions
Technique: $x^2 = 25$ becomes $x = ±\sqrt{25} = ±5$
Check: Verify both values: $5^2 = 25$ and $(-5)^2 = 25$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative solution when taking square roots
Don't just write $x = \sqrt{25} = 5$ and stop there = missing half the answer! The square of both positive and negative numbers gives positive results. Always include both $x = +5$ and $x = -5$ when solving $x^2 = 25$ .

Practice Quiz

Test your knowledge with interactive questions

Complete:

The missing value of the function point:

$$ f(x)=x^2 $$

$$ f(?)=16 $$

FAQ

Everything you need to know about this question

Why are there two answers for x when y = 25?

Because squaring eliminates the sign! Both $5^2$ and $(-5)^2$ equal 25. When you reverse the process by taking the square root, you must consider both possibilities.

How do I remember to include both positive and negative solutions?

Always write the ± symbol immediately when taking square roots: $x = ±\sqrt{25}$ . This reminds you that square roots have two values!

What does the graph of y = x² look like at y = 25?

The parabola $y = x^2$ opens upward. At $y = 25$ , a horizontal line crosses the parabola at exactly two points: $(5, 25)$ and $(-5, 25)$ .

Can x² ever equal a negative number?

No! Squaring any real number (positive or negative) always gives a positive result. So $x^2 = -25$ has no real solutions.

How do I check my answers?

Substitute each value back into the original equation. For our problem: $5^2 = 25 ✓$ and $(-5)^2 = 25 ✓$ . Both work!

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