Given
The table which represents a quadratic equation is,a
To find the options which are true for the quadratic equation.
Explanation:
It is given that,
Then, the quadratic equation is of the form,
[tex]y=ax^2+bx+c[/tex]
Put x=0 and y=5 in the above equation.
That implies,
[tex]\begin{gathered} 5=a(0)^2+b(0)+c \\ 5=c \end{gathered}[/tex]
Then, the quadratic equation becomes,
[tex]y=ax^2+bx+5[/tex]
Put x=-1, y=7 and x=1, y=7 in the above equation.
That implies,
[tex]\begin{gathered} 7=a(-1)^2+b(-1)+5 \\ 7=a-b+5\text{ \_\_\_\_\_\_\_\_\lparen1\rparen} \\ 7=a(1)^2+b(1)+5 \\ 7=a+b+5\text{ \_\_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]
Adding (1) and (2) implies,
[tex]\begin{gathered} 2a+10=14 \\ 2a=14-10 \\ 2a=4 \\ a=\frac{4}{2} \\ a=2 \end{gathered}[/tex]
And,
[tex]\begin{gathered} 7=2-b+5 \\ 7=-b+7 \\ b=0 \end{gathered}[/tex]
Hence, the quadratic equation is,
[tex]y=2x^2+5[/tex]
Now,
That implies,
The graph is opened up and the graph has one x-intercept.
