Sarvesh K Verma Solutions for Chapter: Theory of Equations, Exercise 2: Practice Exercise

For a quadratic graph, the axis of symmetry and $\mathrm{Y}$-axis coincide (or overlap) then,

For the quadratic equation $3{\mathrm{x}}^2+12\mathrm{x}+10=0,$ what is the vertex of the graph?

For the quadratic equation ${\mathrm{x}}^2+12\mathrm{x}+20=0,$ how far is the vertex from the $\mathrm{X}$-axis?

For the quadratic equation ${\mathrm{x}}^2-11\mathrm{x}+24=0,$ what will be the position of the vertex of the quadratic graph with reference to the $\mathrm{X}$-axis?

For the quadratic equation ${\mathrm{x}}^2+9\mathrm{x}+18=0,$ what will be the position of the vertex of the quadratic graph with reference to the origin (or intersection of both the axes) ?

Find the value of $\mathrm{y}$ where the graph of $3{\mathrm{x}}^2+19\mathrm{x}-18=0$ intersects the $\mathrm{Y}$-axis.

Which of the following is false?

$\left(\mathrm{i}\right)$ If only the positive values of $\mathrm{x}$ are taken, the quadratic graph does not intersect the $\mathrm{Y}$-axis.

$\left(\mathrm{ii}\right)$ If only negative values are taken, the quadratic graph does not intersect the $\mathrm{Y}$-axis.

$\left(\mathrm{iii}\right)$ The interception of $\mathrm{Y}$-axis can be known when we substitute $\mathrm{x}=0,$ in the quadratic function.

$\left(\mathrm{iv}\right)$ There can be minimum zero and maximum two $\mathrm{x}$-intercepts.

If $\mathrm{D}$ be the discriminant of the quadratic equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0,$ what will be the coordinates of its vertex?