Question
Find the vertex of 𝑦 = 𝑥^2 − 3𝑥 − 10
Answers
GPT 3.5
To find the vertex of the quadratic function 𝑦 = 𝑥^2 − 3𝑥 − 10, we need to use the formula for the x-coordinate of the vertex, which is given by 𝑥 = -𝑏/2𝑎, where 𝑎 is the coefficient of the quadratic term and 𝑏 is the coefficient of the linear term.
In this case, 𝑎 = 1 and 𝑏 = -3, so substituting these values into the formula, we get:
𝑥 = -(-3)/2(1) = 3/2 = 1.5
To find the y-coordinate of the vertex, we substitute this value of 𝑥 back into the equation:
𝑦 = (1.5)^2 - 3(1.5) - 10
= 2.25 - 4.5 - 10
= -12.25
Therefore, the vertex of 𝑦 = 𝑥^2 − 3𝑥 − 10 is (1.5, -12.25).
In this case, 𝑎 = 1 and 𝑏 = -3, so substituting these values into the formula, we get:
𝑥 = -(-3)/2(1) = 3/2 = 1.5
To find the y-coordinate of the vertex, we substitute this value of 𝑥 back into the equation:
𝑦 = (1.5)^2 - 3(1.5) - 10
= 2.25 - 4.5 - 10
= -12.25
Therefore, the vertex of 𝑦 = 𝑥^2 − 3𝑥 − 10 is (1.5, -12.25).