Discover the Symmetrical Axis in -3x^2 + 3: A Quadratic Analysis

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

f(x)=3x2+3 f(x)=-3x^2+3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the axis of symmetry for the function
00:03 The axis of symmetry is the X value at the vertex point
00:06 The point where if you fold the parabola in half, both halves are identical
00:09 Let's look at the function's coefficients
00:21 We'll use the formula to calculate the vertex point
00:32 We'll substitute appropriate values according to the given data and solve for X at the point
00:43 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

f(x)=3x2+3 f(x)=-3x^2+3

2

Step-by-step solution

To find the axis of symmetry for the quadratic function f(x)=3x2+3 f(x) = -3x^2 + 3 , we follow these steps:

  • Identify coefficients: Here, a=3 a = -3 , b=0 b = 0 , and c=3 c = 3 .
  • Use the axis of symmetry formula for a quadratic ax2+bx+c ax^2 + bx + c given by x=b2a x = -\frac{b}{2a} .
  • Substitute b=0 b = 0 and a=3 a = -3 into the formula: x=02×(3) x = -\frac{0}{2 \times (-3)} .
  • This simplifies to x=0 x = 0 .

The axis of symmetry for the quadratic function f(x)=3x2+3 f(x) = -3x^2 + 3 is therefore x=0 x = 0 .

3

Final Answer

x=0 x=0

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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