What is the axis of symmetry and vertex for the graph $y = x^{2} + 5 x - 7$ $y=x^2+5x-7$ ?

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Answer 1 · 2017-03-17T04:41:30

Vertex $\Rightarrow (- \frac{5}{2}, - \frac{53}{4})$ $rArr (-5/2,-53/4)$

Axis of Symmetry $\Rightarrow x = - \frac{5}{2}$ $rArr x =-5/2$

Method 1-
The graph of $y = x^{2} + 5 x - 7$ $y=x^2+5x-7$ is -
graph{x^2+5x-7 [-26.02, 25.3, -14.33, 11.34]}
According to the above graph, We can find the vertex and axis of symmetry of the above graph.
Vertex $\Rightarrow (- \frac{5}{2}, - \frac{53}{4})$ $rArr (-5/2,-53/4)$
Axis of Symmetry $\Rightarrow x = - \frac{5}{2}$ $rArr x =-5/2$
Method 2-

Check the derivative of the function.

$y = x^{2} + 5 x - 7$ $y=x^2+5x-7$

$y' = dy/dx = 2x+5$

The derivative of the function is zero at its vertex .

$y' = 2x+5 = 0$

$x=-5/2$

Put the $x=-5/2$ in the function to get the value of the function at $x=-5/2$ .

$y=25/4-25/2-7$

$y=(25-50-28)/4$

$y = -53/4$

Vertex $rArr (-5/2,-53/4)$

Axis of Symmetry $rArr x =-5/2$

The given function is a quadratic function.

$y=x^2+5x-7$

The vertex of the parabola of the quadratic function $= (-b/(2a), -D/(4a))$

$= (-5/(2), -53/(4))$

Axis of Symmetry $rArr x =-5/2$

What is the axis of symmetry and vertex for the graph y=x^2+5x-7y=x2+5x−7y=x^2+5x-7?