Question

which statement is true concerning the vertex and axis of symmetry of ( h(x) = -2x^2 + 8x )?

• the vertex is at ( (0, 0) ) and the axis of symmetry is ( x = 2 ).
• the vertex is at ( (0, 0) ) and the axis of symmetry is ( y = 2 ).
• the vertex is at ( (2, 8) ) and the axis of symmetry is ( x = 2 ).
• the vertex is at ( (2, 2) ) and the axis of symmetry is ( y = 2 ).

Explanation:

Step1: Find x-coordinate of vertex

For quadratic $ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=-2, b=8$, so $x=-\frac{8}{2(-2)}=2$.

Step2: Find y-coordinate of vertex

Substitute $x=2$ into $h(x)$: $h(2)=-2(2)^2+8(2)=-8+16=8$.

Step3: Identify axis of symmetry

Axis of symmetry is $x =$ vertex x-coordinate: $x=2$.

Answer:

The vertex is at (2, 8) and the axis of symmetry is x = 2.