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

Given the expression of the quadratic function

Finding the symmetry point of the function

$f(x)=-4x^2+8x+3$

Video Solution

Solution Steps

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 coefficients

00:13 We'll use the formula to calculate the vertex point

00:16 We'll substitute appropriate values according to the given data and solve for X at the point

00:28 This is the X value at the point of symmetry

00:31 Now we'll substitute this X value in the function to find the Y value at the point

00:47 This is the Y value at the point of symmetry

00:50 And this is the solution to the question

Step-by-Step Solution

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 $(1, 7)$ .