# How do you write a quadratic function in intercept form who has x intercepts -2, 1.5 and passes through points (4, 7.5)?

Sep 14, 2017

$y = \frac{1}{2} \left(x + 2\right) \left(x - 1.5\right)$

#### Explanation:

#"given the x-intercepts (roots ) of a quadratic function"

$\text{say "x=b " and } x = c$

$\text{then the factors are "(x-b)" and } \left(x - c\right)$

$\text{and the function is the product of the factors}$

$y = a \left(x - b\right) \left(x - c\right) \leftarrow \text{ a is a multiplier}$

$\text{a can be found if we are given a point on the curve}$

$\text{here the x-intercepts are "x=-2" and } x = 1.5$

$\Rightarrow \text{factors are "(x+2)" and } \left(x - 1.5\right)$

$\Rightarrow y = a \left(x + 2\right) \left(x - 1.5\right)$

$\text{to find a substitute "(4,7.5)" into the function}$

$7.5 = a \times 6 \times 2.5 = 15 a \Rightarrow a = \frac{1}{2}$

$\Rightarrow y = \frac{1}{2} \left(x + 2\right) \left(x - 1.5\right) \leftarrow \textcolor{red}{\text{ in intercept form}}$