Find the range of the given function.
-$$f ( x ) = x ^ { 2 } - 3 x + 2$$
A) $\left[ - \infty , \frac { 1 } { 4 } \right]$
B) $\left[ - \frac { 1 } { 4 } , \infty \right]$
C) $\left[ - \infty , \frac { 35 } { 4 } \right]$
D) $\left[ \frac { 35 } { 4 } , \infty \right)$

Question

Quizplus · Accepted Answer

The function $f(x) = x^2 - 3x + 2$ is a quadratic function that opens upwards (since the coefficient of $x^2$ is positive). To find its range, we need to find the vertex of the parabola, which gives the minimum value of the function. The vertex formula for a quadratic function $ax^2 + bx + c$ is given by $-\frac{b}{2a}$. Substituting $a = 1$ and $b = -3$, we get the x-coordinate of the vertex as $\frac{3}{2}$. Substituting this back into the function gives the minimum value: $f\left(\frac{3}{2}\right) = \left(\frac{3}{2}\right)^2 - 3\left(\frac{3}{2}\right) + 2 = \frac{9}{4} - \frac{9}{2} + 2 = -\frac{1}{4}$. Therefore, the range of the function is $\left[ - \frac { 1 } { 4 } , \infty \right]$.

Find the Range of the Given Function f(x)=x2−3x+2f ( x ) = x ^ { 2 } - 3 x + 2f(x)=x2−3x+2

Find the Range of the Given Function $f ( x ) = x ^ { 2 } - 3 x + 2$