Solve y=x² When y=4: Finding X-Coordinates

Quadratic Functions with Positive and Negative Solutions

What is the value of X for the function?

y=x2 y=x^2

of the point y=4 y=4 ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Set up and solve
00:06 Let's substitute appropriate values according to the given data, and solve for X
00:12 Extract the root
00:15 When extracting a root there are 2 solutions, positive and negative
00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the value of X for the function?

y=x2 y=x^2

of the point y=4 y=4 ?

2

Step-by-step solution

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

  • Step 1: Set the equation of the function with the given point, x2=4 x^2 = 4 .
  • Step 2: Solve for x 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 x2=4 x^2 = 4 .

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

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

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

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

3

Final Answer

Answers a + b

Key Points to Remember

Essential concepts to master this topic
  • Square Root Property: When x2=a x^2 = a , then x=±a x = \pm\sqrt{a}
  • Technique: From x2=4 x^2 = 4 , we get x=±2 x = \pm 2 (both positive and negative)
  • Check: Substitute both values: (−2)2=4 (-2)^2 = 4 and (2)2=4 (2)^2 = 4 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting the negative solution when taking square roots
    Don't just write x=2 x = 2 when solving x2=4 x^2 = 4 = missing half the answer! Squaring either 2 or -2 gives 4, so both are valid solutions. Always remember x=±4 x = \pm\sqrt{4} gives two solutions.

Practice Quiz

Test your knowledge with interactive questions

What is the value of y for the function?

\( y=x^2 \)

of the point \( x=2 \)?

FAQ

Everything you need to know about this question

Why are there two answers when solving x2=4 x^2 = 4 ?

+

Because both positive and negative numbers give the same result when squared! Both 22=4 2^2 = 4 and (−2)2=4 (-2)^2 = 4 , so the parabola y=x2 y = x^2 intersects the line y=4 y = 4 at two points.

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

+

Always use the plus-minus symbol (±) when taking square roots! Write x=±4 x = \pm\sqrt{4} as your first step, then simplify to get both x=2 x = 2 and x=−2 x = -2 .

What does 'Answers a + b' mean in the multiple choice?

+

This means both answer choice a and answer choice b are correct. Since we found two solutions (x=−2 x = -2 and x=2 x = 2 ), we need both individual answers combined.

Can I check my work by substituting back?

+

Absolutely! Substitute both solutions: y=(−2)2=4✓ y = (-2)^2 = 4 ✓ and y=(2)2=4✓ y = (2)^2 = 4 ✓ . If both give y=4 y = 4 , you've got it right!

Why isn't x=4 x = 4 correct?

+

Because 42=16 4^2 = 16 , not 4! Students often confuse the value of y with the solution for x. Remember: we're solving for the x-coordinates where the parabola reaches height 4.

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