Find the vertex of a parabola using completing square method X²−8X+10

Question

ScanSolve AI Tutor · Accepted Answer

To find the vertex of the parabola X² − 8X + 10 using the completing the square method, we want to transform the expression into the vertex form a(X−h)² + k, where (h, k) is the vertex. Step 1: Start with the given quadratic expression. X² − 8X + 10 Step 2: Focus on the X² − 8X part to complete the square. Take half of the coefficient of X (which is −8), square it, and add and subtract it. Half of −8 is −4. (−4)² = 16. So, we add and subtract 16: X² − 8X + 16 − 16 + 10 Step 3: Group the perfect square trinomial and simplify the constant terms. (X² − 8X + 16) − 16 + 10 The expression inside the parenthesis is a perfect square: (X−4)². (X−4)² − 6 Step 4: Identify the vertex from the vertex form a(X−h)² + k. In our case, the expression is (X−4)² − 6. Comparing this to a(X−h)² + k, we have a=1, h=4, and k=−6. The vertex of the parabola is (h, k). The vertex is (4, −6).

Find the vertex of a parabola using completing square method X²-8X+10

Answer

Step-by-step solution

Start with the given quadratic expression.

Focus on the $X^2 - 8X$ part to complete the square.

Group the perfect square trinomial and simplify the constant terms.

Identify the vertex from the vertex form $a(X-h)^2 + k$ .

Try one yourself

Still stuck on this one?

More Mathematics Questions