Question

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

The axis of symmetry of a quadratic function can be found by using the equation $x=-\frac{b}{2a}$.

Short answer

The sentence, “The axis of symmetry of a quadratic function can be found by using the equation is $x=-\frac{b}{2a}$” is true.

Step-by-step solution

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $y=a{x}^2+bx+c$, where, $a\ne 0$is called the standard form of the quadratic function.

Step 2. Define the axis of symmetry of the quadratic function.

The axis of symmetry is the vertical line that goes through the vertex of the quadratic function.

Step 3. Check whether the given sentence is true or false.

If the quadratic equation is given by $y=a{x}^2+bx+c$, then the axis of symmetry is $x=-\frac{b}{2a}$.

Therefore, the sentence, “The axis of symmetry of a quadratic function can be found by using the equation is $x=-\frac{b}{2a}$” is true.