Use the vertex and intercepts to sketch the graph of the quadratic function f(x)=2x2−4x−6. Give the equation for the parabola's axis of symmetry.

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Use the vertex and intercepts to sketch the graph of the quadratic function f(x)=2x2−4x−6. Give the equation for the parabola&#039;s axis of symmetry.

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Given equation is f(x)=2x2–4x–6.     It can be written as y=2x2−4x−6    Here, a=2, b=−4, c=−6    We can see that a&amp;gt;0, so it will be upward parabola.    Since it is upward parabola, so vertex will be its minimum point.     We know that x coordinate of vertex is given x=−b2a    x=−−42⋅2    So, x coordinates of vertex is 1.     Now, put x=1 in the given equation, we get     y=2(1)2–4⋅1−6    =2−10    =−8    Therefore, vertex is (1,–8).  NSК  Now, we have to find intercepts.     For y intercepts , we will put x=0    y=2(0)2–4⋅0−6    =−6  Therefore, y intercepts will be (0.−6)     For the x-intercepts, y=0     Therefore, we will have     2x2–4x–6=0    2x2–6x+2x–6=0    2x(x–3)+2(x−3)=0    (x–3)(2x+2)=0    (x–3)(x+1)=0    So, x−3=0⇒x=3 and x+1=0⇒x=−1    So, the x-intercepts are (−1,0) and (3,0).    The given equation y=2x2–4x–6 can be written as:     y=2(x2–2x–3)    =2((x–1)2–4)    =2(x–1)2–8    We know that if the equation of parabola is y=a(x–b)2+c then    axis of symmetry is given as x=b.     Hence, the axis of symmetry for given parabola will be x=1.

Use the vertex and intercepts to sketch the graph of the quadratic function f

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