Find the Axis of Symmetry in Quadratic Equation -5x² + 10

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=5x2+10 f(x)=-5x^2+10

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the point of symmetry in the function
00:03 The point of symmetry is the point where if you fold the parabola in half
00:06 The halves will be equal to each other
00:10 Let's examine the function's coefficients
00:14 We'll use the formula to calculate the vertex point
00:17 We'll substitute appropriate values according to the given data and solve for X at the point
00:20 This is the X value at the point of symmetry
00:26 Now we'll substitute this X value in the function to find the Y value at the point
00:38 This is the Y value at the point of symmetry
00:43 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

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=5x2+10 f(x)=-5x^2+10

2

Step-by-step solution

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

  • Step 1: Identify the coefficients a a , b b , and c c from the quadratic function.
  • Step 2: Apply the vertex formula to find the x-coordinate of the symmetry point.
  • Step 3: Substitute the x-coordinate back into f(x) f(x) to find the y-coordinate of the vertex.
  • Step 4: Conclude the symmetry point as the vertex, (x,f(x))(x, f(x)).

Now, let's work through each step:

Step 1: The quadratic function is f(x)=5x2+10 f(x) = -5x^2 + 10 . The coefficients are a=5 a = -5 , b=0 b = 0 , and c=10 c = 10 .

Step 2: Applying the vertex formula x=b2a x = -\frac{b}{2a} , we have:

x=02(5)=0 x = -\frac{0}{2(-5)} = 0 .

Step 3: Substitute x=0 x = 0 back into the function:

f(0)=5(0)2+10=10 f(0) = -5(0)^2 + 10 = 10 .

Step 4: Therefore, the vertex and symmetry point of the function is (0,10)(0, 10).

The correct choice from the given options is (0,10)(0,10).

Therefore, the solution to the problem is (0,10) (0,10) .

3

Final Answer

(0,10) (0,10)

Practice Quiz

Test your knowledge with interactive questions

Given the expression of the quadratic function

Finding the symmetry point of the function

\( f(x)=-5x^2+10 \)

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