How do i find the $x - intercepts$ of a quadratic function in vertex form ${(x + 4.5)}^{2} - 6.25$ ?

Open in App

Solution

Find the $x$ -intercepts of the given quadratic function:
Given, a quadratic function, $y = {(x + 4.5)}^{2} - 6.25$
To find $x - intercepts$ , put $y = 0$ in the equation above:
$\begin{array}{rcl} {(x + 4.5)}^{2} - 6.25 & = & 0 \\ \Rightarrow & {(x + 4.5)}^{2} = 6.25 \\ \Rightarrow & x + 4.5 = \pm \sqrt{6.25} \\ \Rightarrow & x + 4.5 = \pm 2.5 \\ \Rightarrow & x = \pm 2.5 - 4.5 \\ \Rightarrow & x = (2.5 - 4.5) or (- 2.5 - 4.5) \\ \Rightarrow & x = - 2 or - 7 \end{array}$
Therefore, the $x - intercepts$ of the given quadratic function are $- 2$ and $- 7$ .

Suggest Corrections

Similar questions

How do you find the vertex of a quadratic equation?

How do you find the $x - intercepts$ of a quadratic function?

What is vertex of a quadratic equation? How do we find it?

How do you write the quadratic function in standard form $y = 4 {(x - 1)}^{2} + 5$ ?

Explain how you could write a quadratic function in a factored form that would have a vertex with an $x -$ coordinate of $3$ and two distinct roots.

Join BYJU'S Learning Program