Additional Concepts
-$$y = x ^ { 2 } - 2 x + 7$$
A) Domain: $( - \infty , \infty )$
Range: $[ 6 , \infty )$
B) Domain: $( - \infty , \infty )$
Range: $( 6 , \infty )$
C) Domain: $( 6 , \infty )$
Range: $( - \infty , \infty )$
D) Domain: $[ 6 , \infty )$
Range: $( - \infty , \infty )$

Question

Additional Concepts
-$$y = x ^ { 2 } - 2 x + 7$$
A) Domain: $( - \infty , \infty )$
Range: $[ 6 , \infty )$
B) Domain: $( - \infty , \infty )$
Range: $( 6 , \infty )$
C) Domain: $( 6 , \infty )$
Range: $( - \infty , \infty )$
D) Domain: $[ 6 , \infty )$  
Range: $( - \infty , \infty )$

Quizplus · Accepted Answer

The equation $y = x^2 - 2x + 7$ is a quadratic function, which means its graph is a parabola. The domain of any quadratic function is all real numbers, $(-\infty, \infty)$, because you can plug any real number into the function for $x$. The range depends on the direction the parabola opens and its vertex. This parabola opens upwards (since the coefficient of $x^2$ is positive), and its vertex can be found using the formula $-\frac{b}{2a}$ for $x$ and plugging that back into the equation for $y$. Here, $a = 1$ and $b = -2$, so the vertex is at $x = 1$, giving $y = 1^2 - 2(1) + 7 = 6$. Therefore, the lowest point on the parabola is at $y = 6$, making the range $[6, \infty)$.

Additional Concepts - y=x2−2x+7y = x ^ { 2 } - 2 x + 7y=x2−2x+7

Additional Concepts
- $y = x ^ { 2 } - 2 x + 7$