Q11. - Algebra 1

Question

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

 $-x^2+3x-1=0$

Step-by-Step Solution

Answer

The roots of the equation $-x^2+3x-1=0$ are $\mathit{x}\mathbf{=}\mathbf{0}\mathbf{.4}$ and $\mathit{x}\mathbf{=}\mathbf{2}\mathbf{.6}$.

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

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

Step 2. Rewrite the equation − x 2 + 3 x − 1 = 0 in the form f x = a x 2 + b x + c .

Write the equation $-x^2+3x-1=0$ in standard form.

This equation is already in standard form.

Write the equation $-x^2+3x-1=0$ in the form $f\left(x\right)=a{x}^2+bx+c$.

 $f\left(x\right)=-x^2+3x-1$$f\left(x\right)=-x^2+3x-1$

Step 3. Plot the graph of the function f x = − x 2 + 3 x − 1 .

The graph of the function $f\left(x\right)=-x^2+3x-1$  is shown below.

Step 4. Solve the equation − x 2 + 3 x − 1 = 0 from the graph of the function f x = − x 2 + 3 x − 1 .

Observe the graph of the function $f\left(x\right)=-x^2+3x-1$.

The graph intersects the  $x$- axis at the points near about  $x=0.4$ and $x=2.6$.  

Therefore the roots of the equation $-x^2+3x-1=0$ are $x=0.4$ and $x=2.6$.  

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