Question

find the x- coordinates of the points where the graph crosses the x-axis.
30.
$y = 4x^2 + 11x - 3$
32.
$y = -3x^2 + 14x + 5$

Explanation:

Step1: Set y=0 for first function

$4x^2 + 11x - 3 = 0$

Step2: Factor first quadratic

$(4x - 1)(x + 3) = 0$

Step3: Solve for x (first function)

$4x - 1 = 0 \implies x = \frac{1}{4}$; $x + 3 = 0 \implies x = -3$

Step4: Set y=0 for second function

$-3x^2 + 14x + 5 = 0$

Step5: Multiply by -1, factor quadratic

$3x^2 - 14x - 5 = 0 \implies (3x + 1)(x - 5) = 0$

Step6: Solve for x (second function)

$3x + 1 = 0 \implies x = -\frac{1}{3}$; $x - 5 = 0 \implies x = 5$

Answer:

For $y=4x^2+11x-3$: $x = -3$ and $x = \frac{1}{4}$
For $y=-3x^2+14x+5$: $x = -\frac{1}{3}$ and $x = 5$