Use a graphing calculator to find the vertex and intercepts for the equation. If your answers are not exact, round to the
nearest tenth.
-$$y = x ^ { 2 } - 7.4 x + 7.87$$
A) $x$-intercepts: $( 1.3,0 )$ and $( 6.1,0 )$; -intercept: $( 0,7.87 )$; Vertex: $( - 7.4,7.9 )$
B) x-intercepts: $( 1.3,0 )$ and $( 6.1,0 ) ; y$-intercept: $( 0,7.87 )$; Vertex: $( 3.7 , - 5.8 )$
C) x-intercepts: $( 1.3,0 )$ and $( 6.1,0 ) ; y$-intercept: $( 0 , - 7.87 )$; Vertex: $( 3.7 , - 5.8 )$
D) $x$-intercepts: none; $y$-intercept: $( 0,7.87 )$; Vertex: $( 3.7 , - 5.8 )$

Question

Quizplus · Accepted Answer

The vertex of a parabola in the form $y = ax^2 + bx + c$ can be found using the formula $-\frac{b}{2a}$ for the x-coordinate, and then substituting this value back into the equation to find the y-coordinate. For the given equation $y = x^2 - 7.4x + 7.87$, the vertex is at $x = \frac{7.4}{2} = 3.7$. Substituting $x = 3.7$ into the equation gives the y-coordinate of the vertex. The $y$-intercept is given directly by the constant term $c = 7.87$, and the $x$-intercepts can be found by setting $y = 0$ and solving the quadratic equation, which yields two real solutions, indicating that choice B is correct with its accurate vertex and intercepts.

Use a Graphing Calculator to Find the Vertex and Intercepts y=x2−7.4x+7.87y = x ^ { 2 } - 7.4 x + 7.87y=x2−7.4x+7.87

Use a Graphing Calculator to Find the Vertex and Intercepts $y = x ^ { 2 } - 7.4 x + 7.87$