Locate the Symmetry Point of f(x) = -4x² + 8x + 3

To find the symmetry point of the quadratic function $f(x) = -4x^2 + 8x + 3$, follow these steps:

• Step 1: Identify key parameters
  The function is of the form $f(x) = ax^2 + bx + c$, with $a = -4$, $b = 8$, and $c = 3$.
• Step 2: Find the x-coordinate of the vertex
  Use the formula for the x-coordinate of the vertex: $x = -\frac{b}{2a}$.
  Substitute the values for $b$ and $a$:
  $x = -\frac{8}{2 \times -4} = -\frac{8}{-8} = 1$.
• Step 3: Find the y-coordinate by substituting back into $f(x)$
  Calculate $f(1)$:
  $f(1) = -4(1)^2 + 8(1) + 3 = -4 + 8 + 3 = 7$.
• Step 4: State the symmetry point
  The symmetry point, or vertex, of the function is $(1, 7)$.

Therefore, the symmetry point of the quadratic function $f(x) = -4x^2 + 8x + 3$ is $(1, 7)$.